Class Notes: Unit 6 – Chemical Quantities, Measurement, and Error(Ch. 3 and 10)

Density

Density is the amount of matter (the mass) of an object in a given volume. Samples of two different materials may have the same mass but they may not necessarily have the same volume depending on how tightly their molecules are packed together. For example, 1 kg of metal may take up the space of your hand, while 1 kg of feathers may take up the size of a car.

“Don’t break my heart and forget the density equation”

Something with a high density has a lot of mass in a tiny volume. The molecules are very tightly packed together. The density of a material is a physical property that remains the same no matter how much mass or volume the material is. For example, aluminum foil, an aluminum can, and a cylinder of aluminum all have the density of 3.1 g/cm3. It is aluminum in each case just a different size or shape.

The units of density are (g/cm3) if you are measuring something that is a solid or (g/mL) if you are measuring a fluid (a liquid or a gas). 1 cm3 = 1 mL. For regularly shaped objects, there are generic formulas for determining volume. For example, the volume of a cube is length * width * height and the volume of a cylinder is pi * radius2 * height. If the object is irregularly shaped, one of the best ways to determine the volume is called the “displacement method”. You put the object in a set amount of a fluid and see the amount of a fluid it displaces. For example, if you put an object into 100 mL of water and after you put it in, the water raises to 125 mL, the volume of that object is 25 mL (the volume of water that it displaced).

The density of water is 1 g/mL. Things sink or float in/on water depending on their densities. If they have a density less than 1 (like wood, density = 0.8 g/cm3) they will float. If they have a density greater than 1 (like aluminum, density = 3.1 g/cm3) they will sink.

Error

As careful as you try to be in taking measurements, there is usually some error associated with them. Error is the difference between an experimental value (what you measure in lab) and the accepted value (based on reliable reference materials).

Generally, there are two types of error: systematic and random. Systematic error is error in experimental observations from you using instruments incorrectly or developing or following a procedure incorrectly. If recognized, systematic errors can usually be fixed with a calculation, rather than having to retake the measurement. One example of systematic error would be taking the mass of things on weighing paper without zeroing out the weighing paper first. All of your masses would be the actual mass plus the mass of the weighing paper. It is very difficult for an individual to recognize systematic error. This is true because usually it is an error doesn’t change throughout the experiment and it can be due to the individual using the instrument incorrectly and they may not know their mistake. Although it is difficult to catch systematic error in an experiment, a possible way of reducing it is to compare your measurements to others and to accepted values of the measurement to try and catch any mistakes.

The other type of error is random error. Random error is error in experimental measurements caused by unknown and/or unpredictable changes in the experiment. Some examples of things that can cause random error are: having uncalibrated measuring instruments; using different instruments to measure the same type of thing (ex: 2 balances to measure mass - maybe one is very old or not working properly); or environmental conditions (the lab is really hot one day but cold the next effecting your measurements). The best way to minimize random error is to repeat the measurement multiple times (do many trials). Then you can look at the average, which should hopefully eliminate any unusual circumstances.

Accuracy and precision are two different ways to describe the error associated with measurement. Accuracy describes how “correct” a measured or calculated value is; that is how close to the measured value is to an accepted value. Precision describes the closeness with which several measurements of the same thing agree. For example, if you were shooting arrows at a target and you got one in the bull’s eye, you would say that that was an accurate shot (because it hit the correct spot on the target). If you shot 5 more arrows and they all landed in a clump in the upper right of the target, because they all landed in the same spot they would be precise with each other (because they are all in the same area), but they are not accurate because they are not in the correct area.

Percent error is an indication of how accurate your measurement is. It tells you how far your measured value is from the accepted value in terms of a percent. A low percent error means your measured value was very close to correct. There is never a negative percent error (in the equation, the numerator is in absolute value signs).

Significant Figures (Sig Figs)

When Taking Measurements:One way to communicate how accurate your measurements are is by writing the measurement numbers with the correct number of significant figures. Significant figures are the numbers in a measurement that are meaningful; that can be accurately read off of the instrument being used to take the measurement. The number of significant figures that there are depends on the instrument you are using and how exact you can get a reading from it. You can read as many exact numbers off the instrument as possible based on the scale (markings) on the instruments, then you can guess one more number.

Example: A beaker with markings at 10 and 20 mL and liquid in between.You know that there is more than 10 and less than 20 mL of water (so you know the 1st number in your measurement is a 1 exactly) but beyond that, there are no markings to indicate what the other numbers in the measurement may be. So you can have 1 more number as a guess. Therefore, there would be 2 significant figures in this measurement.

The major scale of an instrument is how much it is from one large line marking to the next. For example, the graduated cylinder on the right has a major scale of 5 mL. The minor scale of an instrument is how much it is from one small line marking to the next. For example, the graduated cylinder on the right has a minor scale of 0.5 mL. (This was found by taking the major scale, 5 mL, and dividing it by the number of minor scale marking that made up the major scale, 10) 5 mL/10 marking = 0.5 mL/marking

Example: A graduated cylinder with major scale markings every 1 mL and minor scale markings every 0.1 mL. See picture to left.You know that there is more than 15 and less than 16 (so you know at least 2 exact numbers from the major scale markings). Then you can also see from the minor scale markings that the liquid is greater than 15.4 but less than 15.5 (so you know 3 sig figs exactly from the markings: 15.4). Now, you can tell no more exact numbers from any markings on the instrument, so you get one more guess number. Therefore, there would be a total of 4 significant figures in this measurement.

When Doing Calculations: You should not have a calculated answer that is more precise than the least precise measurement used to calculate it. The answer to a calculation can have no more significant figures than the value with the least number of sig figs used in the calculation.

Example: If you multiply 7.7 (2 sig figs) by 5.4 (2 sig figs) in your calculator, you get 41.58. However, because both of the values used in the calculation only have 2 sig figs, the answer can only be given with 2 sig figs. So the answer in correct sig figs is 42.

Zeros:A 0 in a measurement or calculation can be significant or insignificant depending on where it is located related to the other digits.

- If the 0 appears between other numbers it is significant (Ex: 409 has 3 sig figs)

- 0s that appear before other digits are insignificant, they are just placeholders (Ex: 0.0071, 0.42, and 0.00000095 all have just 2 sig figs)

- 0s to the right of a number and after the decimal place are significant (Ex: 25.0 has 3 sig figs)

- 0s to the right of a number when there is no decimal places are not significant (Ex: 300 has 1 sig fig but 300.0 has 4 sig figs) In this scenario, rewriting your measurement or calculation answer in scientific notation to only show a certain number of sig figs makes it more clear exactly how many of these numbers are significant (Ex: 300 has 1 sig fig because the 0s after the 3 aren’t significant since there’s no decimal place. A clearer way to show this would be 3x102. This way it is clear that there is only one sig fig – the 3 – but that the measurement is actually 300.

- There are 2 scenarios where a number can have an infinite number of sig figs: counting and defined quantities.

o Ex: Counting – there are 2 people would be the same as there are 2.0000000…. people since you can never have a fraction of this count it is understood to have infinite sig figs

o Ex: Defined Quantity – there are 100 cm in 1 m would be the same as there is 100.0000000…cm in 1.00000…..m since both of these numbers are an exact defined relationship they can both be considered infinite.

Scientific NotationWhen you have a number that is very large or very small, there is a shorter method to express that number rather than writing out all of the digits. This method is known as scientific notation. In scientific notation, a number is rewritten as the product of two numbers: a coefficient and 10 raised to a power.

The larger a number is, the larger the power of 10 needed to represent it. Positive exponents of 10 result in numbers greater than 1 (large numbers). The smaller a number is, the smaller the power of 10 needed to represent it. Negative exponents of 10 result in numbers less than 1 (decimals).

For example: The number 60,200 is equivalent to 6.02 x 10,000 Therefore it can be written in scientific notation as 6.02x104. In summary: 60,200 = 6.02 x 10,000 = 6.02x104

For example: The number 0.0072 is equivalent to 7.2 x 0.001 Therefore it can be written in scientific notation as 7.2x10-3. In summary: 0.0072 = 7.2 x 0.001 = 7.2x10-3

Another way that you may have learned before to determine what power of 10 is used in scientific notation is to count how many places the decimal is moved. However, you should understand the other method mentioned above.

Example: In 60,200 to get to the scientific notation coefficient of 6.02, the decimal was moved 4 places to the left (10 raised to the

4th) Example: In 0.0072 to get to the scientific notation coefficient of 7.2, the

decimal was moved 3 places to the right (10 raised to the -3rd)

Uncertainty

Uncertainty is an estimate of how close your last estimated significant figure is to the accurate value. Uncertainty is an estimate of the error in your measurement. Uncertainty is often represented by the symbol ± (plus or minus), followed by an amount. The general guideline for what the uncertainty of a measurement is, is that uncertainty is up to ½ the minor scale of the instrument. For example, if you had a graduated cylinder with a minor scale of 1 mL, the uncertainty would be ± 0.5 mL.

Some instruments, such as electronic balances, give a direct reading - there are no obvious markings or scale divisions. This does not mean that there is no uncertainty, it means that the balance has already estimated the last uncertain number in its measurement. The last digit is still a guess or estimated number. The uncertainty of an electronic balance usually 1 unit up or down in the last digit. For example, if a balance gave you a reading of 5.432 g, the uncertainty is ± 0.001 g. If the balance gave you a reading of 6.78 g, the uncertainty is ± 0.01 g.

10-4 10-3 10-2 10-1 100 101 102 103 104 0.0001 0.001 0.01 0.1 1 10 100 1,000 10,000

Dimensional Analysis (aka: Unit Conversion)

There are many times in math and science when you need to have certain units for certain applications. Sometimes, the units that you collect the data in may not be the same units you would like to use in your equation. There is a system known as “dimensional analysis” or “unit conversion” where you can change one unit into another. This conversion only depends on you knowing some relationship (a conversion factor) between the two units.

Three very common things that scientists measure are distance, mass, and volume. The SI base units for each of these are meters (m) for distance, grams (g) for mass, and liters (L) for volume. Within each of these three base units, conversions are based just on the prefixes.

Prefix Symbol Prefix How many in 1 base unit?M mega- 0.000001 or 10-6

k kilo- 0.001 or 10-3

(none) base unit (none) base unit 1c centi- 100 or 102

m milli- 1000 or 103

μ micro- 1,000,000 or 106

n nano- 1,000,000,000 or 109

For example, if you want to convert mm to m, you need to know the relationship that there are 1000 mm in 1 m. If you wanted to convert mm to km, you can use two relationships to get there - you know that there are 1000 mm in 1 m and that there are .001 km in 1 m.

The basic set up for dimensional analysis is a series of fractions that you put your known relationships into and then multiply together. The first fraction is always what you are given over 1. You should never start with a relationship, unless that is your only option. Most relationships are conversion factors used in later fractions. In the second fraction, you put the units that you are converting from on the bottom and the base unit on the top. Then you fill in the numerical relationship between those two. In the third fraction and later, you put the base unit on the bottom so it will cancel out and whatever unit you are trying to convert to on the top. Then you fill in the numerical relationship between the two.

When you have written all your fractions, you multiply through. The top row of the fractions gets multiplied together and divided by the bottom row of the fractions multiplied together. The units get cancelled if they appear on both the top and bottom of the fraction and you should be left with only the units you are trying to convert to.

Ex: How many km are in 30 mm?

When you get an answer you should check to see if it makes sense. Foe the example above, does it make sense that there is a very small number (.00003) of km in 30 mm? It does because a km is much bigger than a mm.

This process can be applied to any base unit: meter, grams, Liters, or any other base unit for the thing you are measuring. These steps generally apply to all situations. However, sometimes the base unit is what you are given or solving for so you can adapt. Just keep in mind that you are trying to cancel one unit to get to another using whatever relationships you can think of.

You can also use dimensional analysis to go between base units as long as you are given or know what the relationship is from one base unit to another.

Ex: The density of water is 1g/1mL. How many mL are in 20 kg of water?

Measuring in ChemistryThere are many instances in chemistry where you want to measure the amount of matter that you have. What are common ways to measure things? There are three basic amounts measurable: the number/count, the mass, and the volume.

** Don’t forget the difference between mass and weight. Mass is the amount of matter in an object. The SI unit for mass is the kg. Weight is the effect of gravity on the mass of an object. Therefore, weight = mass * 9.8 (the gravity on Earth is 9.8 m/s2). The SI unit for mass is the Newton (N). The mass of something never changes no matter what. The weight changes depending on what gravity it is in. For example, if the mass of you is taken on Earth and on the moon, it would be the same. If the weight of you was taken on the Earth and on the moon, you would weight much less on the moon because the force of gravity is much less on the moon. The balances we use in lab give you mass. The scales you use at home give you weight.

For many commonly found numbers we have common words to represent their amount. For example, a dozen is 12 of something and a pair is 2. You can usually relate the common word to each of the three common measurements. For example, a dozen apples is the same as 12 apples (number/count), 2 kg (mass), or 0.2 bushels (volume).

Knowing these count, mass, and volume relationships allow you to convert between units. Often times you can convert commonly known relationships in your head (4 shoes

= 2 pairs, 6 eggs = ½ dozen), however, converting using dimensional analysis will help when you have to do much more complex conversions between things you may not be so familiar with. Previously, we have used dimensional analysis to convert between prefixes of the same base unit; however, if you have the proper conversion factors, you can convert between any units.

The three apples relationships previously mentioned (a dozen apples is the same as 12 apples, 2 kg, or 0.2 bushels) are three conversion factors that you can use to solve problems.

Ex: What is the mass of 90 apples?

Ex: If each apple has 8 seeds, how many seeds are in 14 kg?

Dimensional analysis is commonly used in chemistry to convert an easily measurable value, like mass, to a more obscure (harder to measure) value, like atoms. As long as the conversion factors are known, this is possible.

The MoleMatter is composed of particles, specifically atoms, ions, molecules, and compounds depending on what substance you are dealing with. These particles are very small. Counting one by one is not only impractical but very difficult.

In chemistry, there is a commonly used word to represent a specific number of things too: the mole. The mole unit is written in shorthand as mol.

1 mole (mol) of a substance = 6.02 x 1023 particles of that substance

6.02x1023 is also known as Avogadro’s numbers, after the scientist who clarified the difference between atoms and molecules. Avogadro’s number is always written in scientific notation. Usually a number bigger than x104 (10000) or smaller than x10-4 (.0001) is written in scientific notation. Avogadro’s number is an extremely large number (602 with 23 zeros after it). A lot of 0s may not seem like a big difference but consider this: You live 1 million (1,000,000) seconds in 11.6 days. You live 1 billion (1,000,000,000) seconds in 32 years. That’s just three 0s difference. Think about how many 0s are in Avogadro’s number.

If you stack pennies in a column, it would take 7 stacks to the moon and back to have Avogadro’s number of pennies. If you spend a million dollars a second, it would take you 20 billion years to spend Avogadro’s number of dollars.

The word particle is a general term referring to small pieces of matter. Particle can in fact mean atom, ion, molecule, or compound depending on the specific matter is referring to.

Atom (Ex: Al, N, Fe, Mg, O, etc)Ion (Ex: N-3, Ca+2, Br-1, etc)Molecule (Ex: N2, H2O, C11H22O11, etc) – covalently bonded groups – all nonmet.Compound (Ex: NaCl, MgBr2, etc) – ionically bonded groups – metal/nonmetal

Every 6.02x1023 of any of these particles is 1 mol of the particle. This mole-particle relationship is a commonly used conversion factor.

Ex: How many moles are in 20 atoms of Fe?

Ex: How many moles are in 2.41x1024 compounds of NaCl?

Ex: How many moles are in 10,000 molecules of H2O?

*Notice the difference between mol (the shorthand for moles) and molecules. Molecules is never shortened – to keep it from being confused with moles.

Ex: How many atoms are in 2 moles of H2O?

*Notice here we could not directly convert between moles and atoms, even though that is what the problem was asking for. This couldn’t be done because H2O is not an atom, it is a molecule. Therefore, we have to convert to molecules first. Then we can convert molecules to atoms. Since there are 3 atoms in a molecule of water (2 H’s and 1 O), that is the conversion used in this instance.

The Mass of a MoleThe atomic mass of an atom is represented by the amu (atomic mass unit). The amu is based on C-12 and ever other element’s amu is relative to C-12 and this ratio is always the same. H=1 amu, Li = 7 amu, C = 12 amu, Ne = 20 amu, etc. For example, a carbon atom has 12 times more mass that an atom of H. If the mass of carbon was 12 g, the mass of hydrogen would be 1 g. Based on the relative ratios, 12 g of C and 1 g of H are both 1 atom.

Since chemists use grams (mass) to easily measure things in the lab, the relative scale of masses (amu) was converted to a relative scale of masses in grams. The atomic mass of an element is equal to the grams in one mole of the element. This g/mol is also known as the “molar mass.”Amu = g / mol

Ex: Molar mass of:Fe = 56 g/molS = 32 g/mol

In finding the molar mass of molecules or compounds, it is the total molar mass of all elements in the compound.

Ex: Molar mass of:H2O = 18 g/mol (H = 1g/mol; O = 16 g/mol)O2 = 32 g/mol (O = 16 g/mol)C11H22O11 = 330 g/mol (C = 12 g/mol; H = 1 g/mol; O = 16 g/mol)Al2(CO3)3 = 234 g/mol (Al = 27 g/mol; C = 12 g/mol; O = 16 g/mol)

Therefore, 1 mol of water is 18 g while 1 mol of sugar (C11H22O11) is 330 g. There are 6.02x1023 particles in each of these two samples but because of the difference in molar mass, there is a difference in mass and, in turn, volume.

Converting from Moles → Mass and Mass → MolesTo convert between moles and mass, the conversion factor is the molar mass of whatever substance you are dealing with (since the molar mass contains both the mole and mass units). Using dimensional analysis to solve these problems allows you to perform these calculations without having to memorize equations.

Ex: What is the mass of 3 mol of NaCl?

Ex: How many moles are in 25 g of H2O?

The molar mass conversion factor can now be combined with Avogadro’s number conversion factor to convert between mass and particles and vice versa.

Ex: How many atoms are in 15 g of Fe?

Ex: What is the mass of 2.8x1020 compounds of MgOH?

Converting from Moles → Volume and Volume → MolesThe volumes of 1 mol of solids and liquids vary greatly depending on how tightly packed the atoms are (the density). For this reason mass is the most common conversion to moles for solids and liquids. The volume of a mole of gases, however, is much more predictable due to the nature of gas behavior and the large space between the gas particles. Therefore, when converting to and from moles of a gas, volume is the conversion factor. Avogadro predicted and proved that equal volumes of gases at the same temperature and pressure have the same number of particles.

Because of gas’ ability to expand or contract based on temperatures and/or pressures, gases are usually compared at a standard temperature and pressure (STP). For gases, the standard temperature is 0°C. For liquids or solids, the standard temperature is 25°C. The standard pressure, for all states, is 1 atmosphere (or 1 atm). At STP, 1 mol of any gas occupies a volume of 22.4 L. This 22.4L is called the “molar volume” of a gas. The unit of molar volume if L/mol.

At STP, all the diatomic molecules are gases (H2, N2, O2, F2, Cl2, Br2, and I2). Other common gases include CO2 and He however there are many other gases at STP.Ex: What volume will 0.375 mol of O2 gas take up at STP?

Ex: How many moles of H2 gas is in 0.2 L?

Challenge Problem:What is the molar mass of 1 mol of O2 at STP given that the density of O2 is 1.43 g/L?

Compare this value with what you would calculate for the molar mass of O2 just using the periodic table. It’s approximately the same (32 g/mol).

Now we have a third conversion factor (molar volume). Combined with molar mass and Avogadro’s number we have the three conversion factors to allow us to convert between any of the three ways of measurement (number, mass, and volume).

Ex: What is the volume of 3g of hydrogen gas?

Ex: How many molecules are in 5 g of water?

Ex: What is the mass of 3.8x1025 atoms of iron?

The Mole Road MapWe have now related the mole to the number of particles, mass, and volume. The mole is the basic conversion unit between these three things and to go from one of these units to another you must go through the mole as an intermediate step. The form of the conversion factor depends on what you start with (what you know) and what you want to calculate.

** You don’t need to memorize these exact equation paths. So long as you know the 3 basic conversion factors (Avogadro’s number, molar mass, and molar volume), use dimensional analysis to create your equation for you.

Percent CompositionThe nature of every element is unique and the type or amount of each element in a compound plays a big role in the compound’s overall properties. Therefore, it is useful to know the percents of the components of a compound. Knowing the percent composition of elements in a compound also allows you to determine the chemical formula of the compound from data, such as mass obtained in an experiment.

The relative amounts of the elements in a compound are expressed as the “percent composition”. This is also known as the percent by mass.

Percent Composition from a Chemical FormulaEx: What is the % composition of the elements in K2CrO4?

Notice that the molar mass of K is 39g. However, there are two atoms of potassium in this compound; therefore the mass of potassium for the percent composition equation is 78 g (39g*2).

The total composition for all the elements must be 100% since these elements are all that the compound is made up of. In this example, 40.2% + 26.8% + 33% = 100.0%

Percent Composition from Mass DataSince percent composition is also the percent by mass, this percent composition can also be used in the analytical lab sense to describe amounts of materials in a reaction.

Ex: You collect 5.4 g of oxygen from the decomposition of 13.6 g of magnesium oxide. What is the percent composition of magnesium oxide?

2MgO → 2Mg + O2

Reactants: MgO = 13.6 g Products: Mg = ? g O2 = 5.4 g

From the law of conservation of mass we know that the mass before and after the reaction must be the same. Therefore, the mass of Mg = 13.6 g - 5.4g = 8.2 g.

To find the percent composition of MgO, you find the percents of each of its elements.

In this situation, we use the actual mass (the number of grams from the experiment) for the masses of the elements and compounds as opposed to the molar masses off the periodic table. It can be done either way so long as you know the formula for the compound you are dealing with. It is good to learn how to do it using actual numbers from the lab for instances where you are not sure the exact chemical formula of the compound. You can actually determine the chemical formula from the percent composition of its elements and we will learn how to do this by the end of the chapter.

Ex: Calculate the percent composition of the compound formed when 9.03 g Mg combine with 3.48 g N.

3Mg + N2 → Mg3N2

Reactants: Mg = 9.03 g Products: Mg3N2 = ? N = 3.48 g

Due to the law of conservation of mass the mass of the product is 9.03 g + 3.48 g = 12.51 g

Percent Composition as a Conversion FactorYou can use % composition to determine the mass of an element in the mass of a compound. Since the percents always add up to 100, you can say that whatever the percent of a specific element is in a compound is what it would be in 100 g. For example, if the percent of N in a compound was 45%, in 100 g of that compound there would be 45 g of nitrogen. Therefore, % composition can also be used as a conversion factor:

% number as g of element / 100 g compound

Ex: What is the mass of carbon in 50 g of C3H8?

There are 81.8 g of carbon in every 100 g of C3H8.

Empirical Formulas

From the percent composition of a compound, you have the basic ratio of the elements in the compound. This basic ratio is known as the “empirical formula.” It is the lowest whole number ratio of the atoms of the elements in a compound. The ratios expressed in formulas are mole ratios.

An empirical formula is always the same as the chemical formula for ionic compounds, since ionic compound formulas are already the lowest whole number ratio. For molecule compounds however, the empirical formula may be different than the chemical formula. For example, hydrogen peroxide has the chemical formula of H2O2 however the empirical formula would just be HO. The actual hydrogen peroxide molecule is H2O2 (2 atoms of hydrogen bonded with 2 atoms of oxygen) however the lowest whole number ratio of the two elements in the compound is 1:1.

Ex: A compound has 25.9% N and 74.1%O. What is the empirical formula of the compound?You are given percent compositions. These tell you the ratio of the mass of N atoms to the mass of O atoms in the compound. You must change this mass ratio to a mole ratio since formulas express ratios in terms of moles. So you are given % and you want to convert that to moles. % can be converted to g by assuming that we have a 100g sample. In a 100 g sample of the substance, the % compositions are directly equal to grams. Therefore, we have 25.9 g of N and 74.1 g of O in our 100 g sample. (It is possible to use other masses of the overall sample; however it makes calculations more difficult). Now, to go from g to mole we use the molar mass.

Now we know the ratio of moles in the compound, N1.85O4.63. Is this the empirical formula? No, because it is not a whole number ratio. How can we turn these numbers into whole numbers? We can divide them both by the smaller number of moles, that will at least make one of them equal to one and we can go from there.

Now we have a ratio of NO2.5. Still not a whole number ratio because the O is 2.5. What can we do to make the 2.5 the lowest whole number possible? Multiply by 2 (2.5*2 = 5). What is done to one element in the compound must be done to the other(s).

1 mol N *2 = 2 mol N 2.50 mol O * 2 = 5 mol ONow our ratio is N2O5 – the lowest whole number ratio possible – the empirical formula.

It is always good to double check that your results make sense when you are done. Does a ratio of 2:5 correlate with the original percent compositions given (25.9:74.1)?

Ex: Find the empirical formula for a compound with 94.1% O and 5.9% H.

Empirical Formula: HO

Ex: Find the empirical formula for a compound with 67.6% Hg, 10.8% S, and 21.6% O.

Empirical Formula: HgSO4

Ex: Find the empirical formula for a compound with 62.1% C, 13.8% H, and 24.1% N.

Empirical Formula: C3H8N

Molecular FormulasIonic compounds by nature are empirical formulas. However, there are many molecules that share the same empirical formula. Therefore, a different type of formula is necessary to distinguish the exact molecule you are talking about: the molecular formula. The molecular formula tells the actual number of each kind of atom present in a molecule of the substance. The molecular formula of a compound in some cases is exactly the same as the empirical formula. Otherwise, it is a whole-number multiple of the empirical formula.

Ex: Empirical: CH, Molecular: C2H2 (ethyne), Molecular: C6H6 (benzene)

To determine the molecular formula of a substance, you must know two things: 1) the empirical formula and 2) the molar mass of the compound (often determined by other experimental methods such as a mass spectrometer).First, from the empirical formula, you find the empirical formula mass (efm). This is simply the molar mass of the empirical formula compound. For example, if our empirical formula was HO, the mass would be (1.0g/mol + 16.0 g/mol) 17.0 g/mol.

Then, you compare the efm to the experimentally determined molar mass of your compound. For this example, let’s say it was 34.0 g/mol.

The actual compound molar mass is twice as big as the efm, therefore, the empirical formula must be multiplied by two to give the molecular formula. Our compound in this case has a molecular formula of H2O2 (hydrogen peroxide).

Ex: What is the molecular formula of a compound whose molar mass is 60.0 g/mol and empirical formula is CH4N.

efm = 12 g/mol + (4*1g/mol) + 14 g/mol = 30 g/mol

Molecular Formula = C2H8N2

Ex: What is the molecular formula of a compound with the empirical formula CClN and a molar mass of 184.5 g/mol?

efm = 12 g/mol + (35.5g/mol) + 14 g/mol = 61.5 g/mol

Molecular Formula = C3Cl3N3

Ex: What is the molecular formula of a compound that is 56.6% K, 8.7% C and 34.7% O and has a mass of 138.2 g/mol?

Empirical Formula: K2CO3

efm = (2 * 39.1 g/mol) + 12 g/mol + (3 * 16 g/mol) = 138.2 g/mol

Molecular Formula = K2CO3