math concepts in chemistry

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SY15102 Friday, November 27, 2015

Chemistry 1 Laboratory 1

The study of chemistry involves taking several

observations.

When gathering information, you may ask questions

like:

“what color?” “what shape?”

“how long” “how much?”

• These observations may either qualitative or

quantitative .

•

Quantitative observations are taken throughmeasurements.

• Measurement is the process of finding out how

many measuring units there are in something.

• Metric system is the most widely used system of

measurements.

SI Units

• The most recent version of metric system is the

International System of Units or SI (created by French

scientist in the 1970s).

• There are two types of units:

– fundamental (or base) units; and

– derived units.

• There are 7 base units in the SI system.


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Powers of ten are used for convenience with smaller

or larger units in the SI system.

Scientific Notation

Scientific Notation is a method used in writing very large orvery small numbers in a simpler way:

A X 10n

where A stands for coefficient number (1 ≤ A


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Evaluate the following expressions:

1) (6.0 x 104) / (3.0 x 102)

2) (1.0 x 103) - (2.5 x 102)

3) (3.47 x 102) + (7.32 x 104)

4) (1.4 x 10-3) x (5.3 x 10-3)

Fundamental Units

Length and Mass

Note the SI unit for length is the meter (m) whereas

the SI unit for mass is the kilogram (kg).

1 kg weighs 2.2046 lbs.

1) A cube of gold metal measures 0.01 cm on a

side. What is this length expressed in

millimeters?

2) A student told the class that she takes 200

mg of vitamin B every day. What is this mass

expressed in grams?


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Temperature

There are three temperature scales:

Kelvin Scale

Used in science.

Same temperature increment as Celsius scale.

Lowest temperature possible (absolute zero) is

zero Kelvin.

Absolute zero: 0 K = −273.15 oC.

Celsius Scale

Also used in science.

Water freezes at 0

o

C and boils at 100

o

C.

Fahrenheit Scale

Not generally used in science.

Water freezes at 32 oF and boils at 212 oF.

To convert:

Which of the following shows the relative

temperatures correctly?

A. 12°C > 310K

B. 15°C > 150K

C. 43°C < 300K

D. 158°C > 450K


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Derived Units

Derived units are obtained from the 7 base SI units.

Example:

Volume

The units for volume are

given by (units of length)3.

SI unit for volume is 1 m3.

We usually use 1 mL = 1 cm3.

Other volume units:

1 L = 1 dm3 = 1000 cm3 =

1000 mL.

Volume Density

• Used to characterize substances.

• Defined as mass divided by volume:

• Units: g/cm3.

• Originally based on mass (the density was defined

as the mass of 1.00 g of pure water).


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What is the mass in grams of a cube of gold if

the length of the cube is 0.500 cm? The densityof gold is 19.32 g/cm3.

A. 2.42 g

B. 1.55 x 102 g

C. 3.86 x 101 g

D. 4.14 x 10-1 g

Uncertainty in Measurement

• All scientific measures are subject to error.

• These errors are reflected in the number of

figures reported for the measurement.

• These errors are also reflected in the observation

that two successive measures of the same

quantity are different.

Precision and Accuracy

• Measurements that are close to the “correct”value are accurate.

• Measurements that are close to each other are

precise.

Precision and Accuracy


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Percentage Error

Percentage Error is a way for scientists to express

how far off a laboratory value is from the commonly

accepted value.

The table above shows the data obtained by four

groups of students during a lab investigation

designed to determine the boiling point of

methanol. The accepted value for the boiling point

of methanol is 78.5oC.

a) Whose data was the most accurate?

b) Whose data was the most precise?

Significant Figures

• The number of digits reported in a measurement

reflect the accuracy of the measurement and theprecision of the measuring device.

• All the figures known with certainty plus one extra

figure are called significant figures.

• In any calculation, the results are reported to the

fewest significant figures (for multiplication and

division) or fewest decimal places (addition and

subtraction).

Rules in Significant Figures

• Non-zero numbers are always significant.

• Zeros between non-zero numbers are alwayssignificant.

• Zeros before the first non-zero digit are not significant.

(Example: 0.0003 has one significant figure.)

• Zeros at the end of the number after a decimal place

are significant.

• Zeros at the end of a number before a decimal place

are ambiguous (e.g. 10,300 g).


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Which statement regarding significant figures is

false?A. Zeros can be significant.

B. The number 50,004 has five significant

figures.

C. When dividing, the answer is determined by

the number of decimal places.

D. When multiplying, the answer is determined

by the number of significant figures.

What is the product of 2.32 centimeters and 1.1

centimeters expressed to the correct number of significant digits?

A. 3 cm2

B. 2.6 cm2

C. 2.55 cm2

D. 2.552cm2

Expressed to the correct number of significant

digits, the sum of two masses is 445 grams.

Which two masses produce this answer?

A. 210.10 g + 235.100 gB. 210.100 g + 235 g

C. 210.1 g + 235.1 g

D. 210.10 g + 235.10 g

In chemistry lab, a student was instructed to findthe density of a rectangular piece of metal. Aftercareful measurement, he recorded a mass of 25.45g and a volume of 5.7 cm3. Using the formuladensity = mass ÷ volume and a calculator, hisanswer was 4.464912 g/cm3. Which of these is thecorrect answer to report for the density of themetal?

A. 4 g/cm3

B. 4.5 g/cm3

C. 4.47 g/cm3

D. 4.465 g/cm3


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Dimensional Analysis or Factor-Label Method

• Method of calculation utilizing a knowledge of units.

• Given units can be multiplied or divided to give the

desired units.

• Conversion factors are used to manipulate units:

Desired unit = given unit × (conversion factor)

• The conversion factors are simple ratios:

Using Two or More Conversion Factors

• Example to convert length in meters to length in inches:

cm2.54

in1

m

cm100mof numberinof Number

incmconversion

cmmconversionmof numberinof Number

Using Two or More Conversion Factors

In dimensional analysis always ask three questions:

• What data are we given?• What quantity do we need?

• What conversion factors are available to take us

from what we are given to what we need?

1) If a raindrop weighs 0.10 mg on average and2.0 x 105 raindrops fall on a lawn everyminute, what mass (in kg) of rain falls on thelawn in 1.0 hr?

2) The recommended adult dose of Elixophyllin®, a drug used to treat asthma, is6.00 mg/kg of body mass. What is the dose inmilligrams for a 121-lb person?


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The End

SCIENTIFIC NOTATION

Express the following quantities in scientific

notation:

a. 158000 km

b. 0.000009782 L

c. 837100000 cm3

d. 6500000000 mm2

e. 0.00593 g

SCIENTIFIC NOTATION SCIENTIFIC NOTATION

Express the following quantities in scientific

notation:

a. 158000 kmb. 0.000009782 L

c. 837100000 cm3

d. 6500000000 mm2

e. 0.00593 g


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SIGNIFICANT FIGURES

Determine the number of significant figures inthe following measurements:

a. 0.0120 m f. 1000 kg

b. 100.5 mL g. 180. mm

c. 101 g h. 0.4936 L

d. 350 cm2 i. 0.020700 s

e. 0.97 km

SIGNIFICANT FIGURES

Round the following quantities to the specified

number of significant figures:

a. 5,487,129 m to three significant figures

b. 0.013479265 mL to six significant figures

c. 31,947.972 cm2 to four significant figures

d. 192.6739 m2 to five significant figures

e. 786.9164 cm to two significant figures

SIGNIFICANT FIGURES

Perform the following calculations, and express

the answer in the correct units and number of

significant figures.

a. (651 cm)(75 cm)

b. 7.945 J + 82.3 J - 0.02 J

c. 7.835 kg / 2.5 L

d. 7.382 g + 1.21 g + 4.7923 g

UNIT CONVERSION

1. How many milliliters of water will it take to fill

a 2 L bottle that already contains 1.87 L of

water?

2. A piece of copper wire is 150 cm long. How

long is the wire in millimeters? How many 50

mm segments of wire can be cut from the

length?


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UNIT CONVERSION

3. The ladle at an iron foundry can hold 8500 kg

of molten iron. 646 metric tons of iron are

needed to make rails. How many ladlefuls of

iron will it take to make 646 metric tons of iron?

(1 metric ton = 1000 kg)

UNIT CONVERSION

4. How many palisade cells from plant leaves

would fit in a volume of 1.0 cm3 of cells if the

average volume of a palisade cell is 0.0147

mm3?

UNIT CONVERSION

5. A person drinks eight glasses of water each

day, and each glass contains 300 mL. How many

liters of water will that person consume in ayear? What is the mass of this volume of water

in kilograms? (Assume one year has 365 days

and the density of water is 1.00 kg/L.)

Four Steps for Solving

Quantitative Problems

A. If a liquid has a density of 1.17 g/cm3, how

many liters of the liquid have a mass of 3.75 kg?


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Four Steps for Solving

Quantitative Problems

B. The radioactive decay of 2.8 g of

plutonium-238 generates 1.0 joule of energy as

heat every second. Plutonium has a density of

19.86 g/cm3. How many calories (1 cal = 4.184 J)

of energy as heat will a rectangular piece of

plutonium that is 4.5 cm x 3.05 cm x 15 cm

generate per hour?

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