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!