Download - States of Matter and Boyle’s Law
STATES OF MATTER AND BOYLE’S LAW
Text 9.1: Page 418-428
Uses of Gases
States of Matter
Examples of States
There are examples of elements that exist in each of the 3 states at the room temperature
What Determine State?
What state each compound is in is dependent on the strength of the intermolecular bonds Bond between molecules in
the solid state are the strongest of the three
Bond between molecules in the gaseous state are the weakest of the three
Kinetic Molecular Theory
Called this because any moving object has kinetic energy The energy of
movement or motion Different states are
associated with different amounts of kinetic energy
Kinetics of Gases?
Movement of Molecules
Molecules can move in 3 directions Translational:
straight line Rotational: spinning Vibrational: back-
and-forth motion of atoms within the molecules
Movement of States
If molecules are restricted to vibrational they will stay as solids and in a ordered state Both gases and liquids
will display all 3 types of motion but to different degrees
Movement Between States
Gas Laws: Boyle’s Law
Is a mathematical equation that describes how pressure alters the volume of a gas
p1v1=p2v2
Gas Laws: Boyle’s Law
Is a mathematical equation that describes how pressure alters the volume of a gas
p1v1=p2v2
What Does this Mean?
Relationship between pressure and volume: As pressure increases, volume decreases i.e. when pressure is doubled, volume is
halved
…as the pressure on a gas increases, the volume of the
gas decreases proportionally, provided that the
temperature and amount of gas stays constant…
What Does this Mean?
Relationship between pressure and volume: As pressure increases, volume decreases i.e. when pressure is doubled, volume is
halved
…as the pressure on a gas increases, the volume of the
gas decreases proportionally, provided that the
temperature and amount of gas stays constant…
Measure Pressure?
Pressure is measures in Pascal’s (Pa) This represents I newton
(N) on an area of 1 m2
Atmospheric pressure = 1000 Pa or 1 kPa
Also at times measured in mm Hg because of an instrument we used to use to measure pressure
STP and SATP
For many years did all calculations at STP (standard temperature and pressure) 0 ⁰ C and 101.325 kPa
Now generally use SATP (standard ambient temperature and pressure 25⁰ C and 100 kPa This is also much closer to many
laboratory conditions
STP and SATP
For many years did all calculations at STP (standard temperature and pressure) 0 ⁰ C and 101.325 kPa
Now generally use SATP (standard ambient temperature and pressure 25⁰ C and 100 kPa This is also much closer to many
laboratory conditions
Practise Problem
A 2.0L party balloon at 98 kPa is taken to a top of a mountain where the pressure is 75 kPa. Assume the temperature is the same. What is the new volume of the balloon? (Page 428)
Homework!
CHARLES', GAY-LUSSAC’S AND COMBINED GAS LAW
Text 9.1: Page 429- 438
Learning Goals
By the end of this class, the students will be able to: Describe how temperature and volume in
gases are related in terms of Charles’ Law and kinetic molecular theory
Describe how temperature and pressure in gases are related in terms of Gay-Lussac’s Law and kinetic molecular theory
Gas Laws: Charles’ Law
Is a mathematical equation that describes how temperature alters the volume of a gas
V1 V2
T1 T 2=
What Does this Mean?
Relationship between temperature and volume: As temperature increases, volume increases i.e. when temperature is doubled, volume is doubled
…as the temperature of a gas increases, the volume of the gas increases proportionally, provided
that the pressure and amount of gas stays
constant…
Temperature
Many times temperature measured in Kelvins Another unit to
measure temperature Measure from absolute
zero Where there is absolutely
no kinetic movement in molecules
K = ⁰ C + 273
Standards
For many years did all calculations at STP (standard temperature and pressure) 273.15 K (0 ⁰ C) and 101.325 kPa
Now generally use SATP (standard ambient temperature and pressure 298.15 K (25⁰ C) and 100 kPa Both of these values of K have more digits
but reduced to 3 significant digits
Practise Problems
A gas inside a cylinder with a movable piston is heated from 25⁰C to 315 ⁰C . What is the new volume of the gas knowing the initial volume was 0.30L? (Text 433)
Gas Laws: Gay-Lussac’s Law
Is a mathematical equation that describes how temperature alters the pressure of a gas
P1 P2
T1 T 2=
What Does this Mean?
Relationship between pressure and temperature: As temperature increases, pressure increases i.e. when temperature is doubled, pressure is doubled
…as the temperature of a gas increases, the pressure of the gas increases proportionally, provided
that the volume and amount of gas stays
constant…
Practise Problems
A sealed storage tank contains argon gas at 18⁰ C and a pressure of 875 kPa at night. What is the new pressure if the tank and its contents warm to 32⁰ C during the day? (Text 435)
Gas Laws: Combined Gas Law
Is a summary mathematical equation that describes how pressure, temperature and volume all interact
P1 V1 P2 V2
T1 T 2=
What Does this Mean?
You can use this equation to remember all three of the other equations. Simple cancel out
the variables that stay constant!
Boyle’s Law
P1 V1 P2 V2
T1 T 2=
Charles’s Law
P1 V1 P2 V2
T1 T 2=
Gay-Lussac’s Law
P1 V1 P2 V2
T1 T 2=
Practise Problems
A balloon contains hydrogen gas at 20⁰ C and a pressure of 100 kPa and a volume of 7.50L. Calculate the volume of the balloon after it rises to an upper atmosphere with a pressure of 28 kPa and a temperature of -36 ⁰ C ? (Text 437)
MIXTURES, PARTIAL PRESSURES AND REACTIONS
Text 10.1-10.2: Pages 460-471
Mixtures of Gases
Many years ago scientists believed that the atmosphere was made of only one chemical compound Antoine Lavoisier (1743-
1794) was the first to give evidence that the atmosphere was made of a mixture of gases
He was also known as the father of modern chemistry
Antoine Lavoisier
He did a series of experiments that involved burning different compounds in the presence of air Based on these experiments
he concluded the atmosphere was made of at least 2 gases
One that supported combustion and one that did not
Antoine Lavoisier
Lavoisier also noticed if he burned something in a sealed container when that container was opened to air would rush in This is because there was a
lower pressure in the container because of the volume of gas consumed in the combustion
John Dalton
John Dalton more specifically did work on the properties of gases He hypothesized
that gas molecules work independently and will produce the same pressure whether in a mixture or on its own
Experimental Design
Dalton’s Law of Partial Pressures From his experiments he came up with his
law…
A partial pressure , p, a gas in a mixture would exert if it were the only gas present in the same volume and at the same temperature
“The total pressure of a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual
gases”
ptotal = p1 + p2 + p3 … pn
Kinetic Molecular Theory… Again?
This law can be explained via kinetic molecular theory The collisions are what
cause the pressure It doesn’t matter what
type of gaseous molecules are causing the collisions, just that a specific number of collisions are happening
Practise Problems
“ A compressed air tank for scuba diving to a depth of 30 m, a mixture with an oxygen partial pressure of 28 atm and a nitrogen partial pressure of 110 atm is used. What is the total pressure of the tank?” (Page 461)
Reactions of Gases
Even though gases occur in mixtures around us, they also can react with one another! But always follow The Law of Combining
Volumes Volumes of gases combine according to
mole ratios“When measured at the same
temperature and pressure, volumes of gaseous reactants and products of chemical reactions are always in simple ratios of whole numbers”
Avogadro’s Theory
Even more fully explained by Avogadro’s Theory “Equal volumes of gases at the same
temperature and pressure contain equal numbers of molecules”
Thus we can still use mole ratios to predict volumes of products produced in chemical equations
Practise Problems
“A catalytic converter in the exhaust system of a car uses oxygen (from the air) to convert carbon monoxide to carbon dioxide, which is released through the tailpipe. If we assume the same temperature and pressure, what volume of oxygen is required to react with 125 L of carbon monoxide produced during a 100km trip?”
(Page 468)
Moles of Gases?!?
We can determine moles of a gas from the volume it takes up Molar volume (MV): is the volume that one
mole of a gas takes up at a specified temperature and pressure
At SATP 24.8 L/mol At STP 22.4 L/moln = V / MV
OrMoles = volume / molar
volume
Practise Problem
“What volume is occupied by 0.024 mol of carbon dioxide gas at SATP?” (Page 469)
IDEAL GAS LAW
Text 9.4: Page 443-445
Make Sense?
One last relationship described how volume and number of moles relate It makes sense that as the number of moles
increases so does the volume it takes up More moles, more molecules, more volume!
v α n
Assumptions…
All calculations we have done have made one main assumption: That we are dealing with
an IDEAL gas An ideal gas is a
hypothetical gas that obeys all the gas laws perfectly under all conditions
An Ideal Gas
The problem is…
They don’t condense into a liquid when cooled
They perfectly graph relationships between pressure, temperature and volume they would have exactly linear relationships
Ideal Gases DONT Exist!
Ideal Gas Law
There is an equation that summarizes the characteristics of ideal gases
P = Pressure in kPa n= Moles in… molesV= Volume in L T= Temperature in KR= 8.31 kPa L/ mol K
PV= nRT
The Gas Constant
R = The Gas Constant 8.31 kPaL/ mol K
The constant of variation that relates the pressure in kPa, volume in L, amount in Moles and Temp in K Of an Ideal Gas
An Example of Ideal Gas Relationships
The Real Gas Equation:
Note: You do not need to know this equation, just that ideal gases don’t exist and they actually behave like:
This is also known as the van der Waals equation
Where: a = is a measure of attraction between particles b = is the average volume of gas particles
(P+ n2a/V2)(V-nb)= nRT
Van Der Waals Again?
This equation is also known as the Van Der Waals equation Taking into account the two
new variables: a = is a measure of
attraction between particles b = is the average volume of
gas particles … Why do you think this is
called the Van Der Waals equation?
Ideal vs. Real Gases
The Difference Between Ideal and Real Gases can be done by calculating the Pressure Difference. In the case below this is the pressure exerted by 0.3000 mol of helium in a 0.2000 L container at -25 °C.
Pnon-ideal - Pideal = 32.152 atm - 30.55 atmPnon-ideal - Pideal = 1.602 atm
Practice Problems
What mass of neon gas should be introduced into an evacuated 0.88L tube to produce a pressure of 90 kPa at 30⁰ C?
(Page 444)
Practice Problems
What amount of methane gas is present in a sample that has a volume of 500 mL at 35.0 ⁰C and 210 kPa?
(Page 445)
Homework!