Introduction to the Gas Laws

CPS Chemistry

What is a Gas?

A state of matter where there is indefinite volume (will fill its container) and indefinite density (can be compressed)

Gasses are fluids, because like liquids they have the ability to flow

Gasses are made up of randomly moving molecules, but are mostly empty space

Temperature

Temperature is the measure of how hot or cold an object is relative to something else

Temperature in a gas relates to the kinetic energy of the molecules, the hotter the temperature, the faster they move

Temperature in gas law problems is always measured Kelvin, convert all temps to K

Standard temperature is 273K

Pressure

Pressure is force/area, N/m2 or a Pascal Pressure is directly proportional to applied

force Pressure is indirectly proportional to area Pressure in gasses is the result of the

number of collisions that the molecules make with the container, so the greater the temperature, the greater the pressure

Pressure cont.

Units of pressure are:torrmm of Hg (millimeters of mercury)atm (atmospheres)

Standard Pressure is:760 torr760 mm of Hg1 atmosphere

Volume

Volume is the amount of space that gasses take up, gasses will fully fill any container that they are in

Two units of volume areCubic centimeters: cc or cm3

Millileters: mL

1 cc = 1 cm3 = 1 mL

Boyles Law

Pressure and volume are inversely proportional, if you increase one, you decrease the other

citation

The equation

P1V1 = P2V2

This works when the temperature is kept constant.

Before you start working with ANY gas law problem, make sure that you have all the same units!

Example 1

You have 2.0L of hydrogen gas at 3.0 atmospheres, you increase the pressure to 12.0 atm, what is your new volume?

Example 2

You have 30cm3 of chlorine gas at 1000 torr you change the volume to 90cm3 what is your new pressure? (solve for torr, mm of Hg and atm)

Charles Law

When pressure is kept constant the relationship between Temperature and volume is

citation

The Formula

The formula is

V1 V2

T1 T2

=

Example 1

If pressure is held constant, and a 2.0L of Neon gas is heated from 0°C to 100°C, what is the new volume?

Example 2

If pressure is held constant, and a 850cc of Argon gas is cooled from 50°C to 10°C, what is the new volume?

Gay-Lussac’s Law

“The pressure of a fixed mass of gas at a constant volume varies directly with the temperature (K).”

If you have a certain amount of gas in a fixed sized container, the pressure will change if the temperature changes.

The formula

P1 = P2

T1 T2

Example 1

A cylinder of compressed gas has a pressure of

4.882 atm on one day. The next day the same

cylinder of gas has a pressure of 4.690 atm and

its temperature is 8°C. What was the

temperature on the previous day in C?

Example 2

The safety limit for a certain can of aerosol

stay is 95°C. If the pressure of the gas in the

can is 2.96 atm when it is 17°C, what will the

pressure be at the safety limit?

Combined Gas Law

When you have all three variables involved (Pressure, Temperature, and Volume) you use the combined gas law

P1V1 P2V2

T1 T2

=

Example 1

A 50 mL sample of fluorine gas at 15°C that rises in temperature to 80°C, if the original pressure is 2 atm and increases to 8 atm, what is the new volume?

Example 2

A 500 cc sample of boron gas at 85°C that cools to 0°C, if the original pressure is 768 torr and increases to 850 torr what is the new volume?

Partial Pressures

The total pressure in a combination of gasses is the sum of all the pressures of each individual gas.

Ptot=P1+P2+P3…

*all gas pressures must be in the same unit

Example 1

The total pressure for air in a scuba tank is 1200 torr, if the oxygen has a pressure of 500 torr, the Nitrogen is 350 torr, what is the pressure of the argon gas component?

Ideal Gas Law

All the prior gas laws involve a combination of pressure, temperature, or volume. The ideal gas law also takes into account the number of molecules of gas involved.

PV=nRT

Ideal gas law cont.

P= pressure = atmospheres

V = volume = Liters

T = temperature = Kelvin

n = number of moles = mol

R = gas constant = .0821 L * atm

mol * K

Example 1

A rigid cylinder with a volume of 10.0 liters is filled with neon gas at a pressure of 250. atm at 30°C, how many moles are in the gas?

Example 2

A 12.0 liter flask at 45°C has 5.00 moles of helium gas, what is the pressure?