Chapter 14 Notes Part I Boyle’s, Charles’ and Gay- Lussac’s Laws Combined Gas Laws

Gas Review

In chapter 13 gases were said to be mostly empty space.In chapter 13 gases were said to be mostly empty space. This gives rise to a property called compressibility.This gives rise to a property called compressibility. The particles in a gas can be forced closer together.The particles in a gas can be forced closer together.

Kinetic Theory Kinetic Energy—Energy that an object has due to motion. The Kinetic Theory states that tiny particles form all matter, and they are constantly in motion.

Gases A gas is composed of particles that are small, hard spheres with almost no volume or particle interaction.

Gases Particles in a gas are in constant motion—they travel straight paths unless they collide with another particle or their container.

Gases All collisions are considered elastic—no energy is lost

Temperature When a substance is heated, the particles speed up, causing faster movement and more collisions. This is a rise in temperature.

Obj. 1…Ideal vs. real gases behavior of ‘ideal gases’ (from kinetic theory)… behavior of ‘ideal gases’ (from kinetic theory)… ~ ______ relationship b/n P and V. ~ ______ relationship b/n P and V. inverse ~ ______ relationship b/n T and V. ~ ______ relationship b/n T and V. ~ ______ relationship b/n T and P. ~ ______ relationship b/n T and P. direct direct however, there are no ‘ideal’ gases in existence. however, there are no ‘ideal’ gases in existence. two properties keep ‘real’ gases from being ‘ideal’… two properties keep ‘real’ gases from being ‘ideal’… ~ real gas particles have distinct volumes ~ real gas particles have distinct volumes ~ real gas particles are slightly attracted to each other… ~ real gas particles are slightly attracted to each other… …there comes a point where V can not get smaller, no matter how much P is applied intermolecular attraction of gas molecules causes gases to occupy less space than assumed by the KT.

Obj. 2-3…STP STP = standard temperature and pressure STP = standard temperature and pressure standard temp = standard temp = ~ 0°C ~ 0°C ~ 273 K ** ~ 273 K ** standard pressure = standard pressure = ~ 1 atm ~ 1 atm ~ kPa ~ kPa ~ 760 mmHg ~ 760 mmHg

There are three relationships between the conditions a gas is in that will be affected by this property.There are three relationships between the conditions a gas is in that will be affected by this property. Pressure and volumePressure and volume Volume and temperatureVolume and temperature Pressure and temperaturePressure and temperature

Boyles Law states that as the volume of a gas is decreased, the amount of pressure is increased at constant temperature.Boyles Law states that as the volume of a gas is decreased, the amount of pressure is increased at constant temperature. (P  V  or P  V  )(P  V  or P  V  ) Mathematically, Mathematically, P 1 V 1 =P 2 V 2

Obj. 4-6…Boyle’s Law relationship b/n P and V is expressed in the Boyle’s Law relationship b/n P and V is expressed in the Boyle’s Law equation. ~ inverse relationship ~ inverse relationship ~ only works if T remains constant! ~ only works if T remains constant! p 1 v 1 = p 2 v 2 p 1 v 1 = p 2 v 2 Ex… Ex… The pressure on 2.5 L of a gas decreases from 105 kPa to The pressure on 2.5 L of a gas decreases from 105 kPa to 40.5 kPa. What is the new volume of the gas? V1 P1 P2 V2 105(2.5) = 40.5 (x) 105(2.5) = 40.5 (x) = 40.5 (x) = 40.5 (x) liters

Why? With less volume, there is greater frequency of the same amount of particles hitting the surface of the container.With less volume, there is greater frequency of the same amount of particles hitting the surface of the container.

Charles Law states that as the temperature of a gas is increased, the volume is also increased at constant pressure. (V  T  or V  T  ) Mathematically: V 1 = V 2 T 1 T 2

Obj. 7-9…Charles’s Law relationship b/n T and V is expressed in the Charles’ Law relationship b/n T and V is expressed in the Charles’ Law equation. ~ direct relationship ~ direct relationship ~ only works if P remains constant! ~ only works if P remains constant! v 1 = v 2 Ex… Ex… If a sample of gas occupies 6.8 L at 125 °C, what will its If a sample of gas occupies 6.8 L at 125 °C, what will its volume be at 38 °C if pressure remains constant? V1 T1 T2 V liters T1T1T1T1 T2T2T2T2 ~ temp. MUST be in Kelvin!!! ~ temp. MUST be in Kelvin!!! (°C ) = 398 K = 311 K = x x = 6.8 (311) 6.8 (311) 398

Why? As the temperature increases, the average kinetic energy of the particles increases.As the temperature increases, the average kinetic energy of the particles increases. This increases the amount of volume needed to maintain the same frequency of collision with the surface of the container.This increases the amount of volume needed to maintain the same frequency of collision with the surface of the container.

Meanwhile... Jaques Charles also noticed that no matter what gas he experimented with, when he extrapolated the volume down on a graph, the temperature was the same: -273 o C!

Kelvin William Thomson (a.k.a. Lord Kelvin) recognized this as the theoretical point at which the average kinetic energy of all substances would be zero. Thus, the concept of absolute zero and the Kelvin scale were born!

K= o C+273

When comparing temperatures during this chapter, they must be in Kelvin, because Celsius is a degreed scale and Kelvin is an absolute scale!

Gay-Lussac’s Law states that as you increase temperature of an amount of gas, its pressure will increase if at a constant volume. (P  T  or P  T  ) Mathematically: P 1 = P 2 T 1 T 2

Obj …Gay-Lussac’s Law relationship b/n T and P is expressed in the Gay-Lussac’s relationship b/n T and P is expressed in the Gay-Lussac’s Law equation. ~ direct relationship ~ direct relationship ~ only works if V remains constant! ~ only works if V remains constant! P 1 = P 2 Ex… Ex… A sample of gas has a pressure of 6.58 kPa at 339 K. What A sample of gas has a pressure of 6.58 kPa at 339 K. What will the temperature be at 4.21 kPa? P1 T1 T2 P x K T1T1T1T1 T2T2T2T2 ~ temp. MUST be in Kelvin!!! ~ temp. MUST be in Kelvin!!! (°C ) = 4.21 x = 339 (4.21) 339 (4.21) 6.58

Why? As the temperature increases, the average kinetic energy of the particles increases, thus they move faster.As the temperature increases, the average kinetic energy of the particles increases, thus they move faster. This increases the frequency of collisions, as well as the amount of force in each collision.This increases the frequency of collisions, as well as the amount of force in each collision.

But wait a minute... NO! There’s a handy, dandy equation that will show you ALL these equations in one! Are you saying that I have to keep ALL these equations straight in my head?

Combined Gas Laws P 1 V 1 P 2 V 2 T 1 T 2 =

When one variable is constant, you can just cross it out, and the equation works for all three laws, as well as for combined problems!

Practice Problem #1 The pressure on 2.5L of anesthetic gas changes from 105 kPa to 40.5 kPa. What will the new volume be if the temperature is constant?

Practice Problem #2 A balloon has a volume of 6.7L at 20 o C. What will its volume be at 350 o C if it is at constant pressure?

Practice Problem #3 The pressure in an automobile tire that has a constant volume is 198 kPa at 27 o C. On a hot sunny day the pressure has risen to 225 kPa. What is the temperature?

Practice Problem #4 A gas at 155 kPa and 25 o C occupies a container with an initial volume of 1.00L. By changing the volume the pressure of the gas increases to 605 kPa as the temperature is raised to 125 o C. What is the new volume?A gas at 155 kPa and 25 o C occupies a container with an initial volume of 1.00L. By changing the volume the pressure of the gas increases to 605 kPa as the temperature is raised to 125 o C. What is the new volume?