Now, a little more about

Gases!

Boyle’s Law

•The volume of a gas is inversely related to the pressure at a constant temperature.

P1V1 = P2V2

Equivalent Units of Pressure

•1 atmosphere

•760 mmHg (aka torr)

•101.3 kPa (kilopascals)

•14.7 psi (pounds per square

inch)

Example -

•A sample of helium gas in a balloon is compressed from 4.0L to 250mL at a constant temperature. If the original pressure of the gas is 210kPa, what will be the pressure of the compressed gas?

Charles’ Law•The volume of a gas is directly

proportional to the temperature at a constant pressure.

V1 = V2

T1 T2

Units for Temperature• Gas Law Equations require

temperature to be measured in Kelvins.

K = °C + 273.15

Example…

•What is the volume of the air in a balloon that occupies 0.620 L at 25°C if the temperature is lowered to 0.0°C?

Gay-Lussac’s Law•The pressure of a gas is

directly proportional to the temperature (K) if the volume remains constant.

•P1 = P2

T1 T2

Example…

•The pressure in an automobile tire is 1.88 atm at 25°C. What will be the pressure in psi if the temperature warms up to 37.0°C?

Combined Gas Law

V1P1 = V2P2

T1 T2

Example…

• An unopened, cold 2.00 L bottle of soda contains 46.0 mL of gas confined at a pressure of 131.96 kPa at a temperature of 5.0°C. If the bottle is dropped into a lake and sinks to a depth at which the pressure is 154 kPa and a temperature of 2.1°C, what will be the new volume of the gas?

STP• Standard Temperature

273 K

•Standard Pressure 1 atm or 760 mmHg

Example…

•A sample of gas has a volume of 2050 mL at 0.95 atm and 36°C. What will be the volume of the gas at STP?

Dalton’s Law of Partial Pressure

• The total pressure of a mixture of gases is equal to the sum of the partial pressures of each component gas.

• Pt = P1 + P2 + P3…

Examples…

• A scuba tank contains a mixture of gases including 0.42 atm N2, 205 torr O2 and 35.5 kPa CO2. What is the total pressure inside the tank in atmospheres?

• A sample of oxygen gas was collected over water at 20.0°C and 731.0 mmHg. What is the pressure of the dry gas?

Graham’s Law of Effusion

• The rates of effusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses.

rateA = √MB

rateB √MA

What is effusion?

•When a gas is confined in a container that has a very small opening, the gas molecules will randomly encounter the opening and pass through it.

example

•Calculate the ratio of effusion between ammonia, NH3, and hydrogen chloride gas.

Avogadro’s Principle

• Equal volumes of gases at the same temperature and pressure contain equal numbers of particles!

• Molar Volume – the volume of 1.0 mol of any gas at STP.1 molgas = 22.4 L (new) = 6.02 x 1023 particles = MM in grams

Examples…

• What size container do you need to hold 0.0459 mol N2 gas at STP?

• How many grams of CO2 gas are in a 2.5 L flask at STP?

• How many atoms of He are present in a 1.75 L balloon?

Ideal Gas Law :PV = nRT

Where P = pressureV = volume in Litersn = number of molsR = ideal gas constantT = temperature (Kelvin)

Calculate R, the Ideal Gas Constant…• 1 mol of gas at STP and molar

volume

• R = 0.0821 atm·L mol·K

= 62.4 mmHg·L mol·K

= 8.314 kPa·L mol·K

Example…

• Calculate the number of moles of gas contained in a 3.0L vessel at 33°C and a pressure of 1.50 atm.

• Determine the Celsius temperature of 2.49 mols of gas contained in a 0.75L vessel at a pressure of 143 kPa.

Variations…

• n = m/M so…

PVM = mRT

• d= m/V so…

PM = dRT

Example…

• Calculate the grams of oxygen gas present in a 2.50L sample kept at 1.66 atm pressure and a temperature of 10.0°C.

• What is the molar mass of a gas that has a density of 1.02g/L at 0.990 atm pressure and 37°C?

Examples…• Calculate the grams of N2

present in a 0.600L sample kept at 765 mmHg and a temperature of 22.0°C.

• What is the density of NH3 at

800 mmHg and 25°C?

Real Gases deviate from ideal behavior under 2 circumstances…

To think of these, refer back to the five assumptions of kinetic theory.

Under what conditions would some of these assumptions not hold true?

Deviations of a real gas

1. Extremely high pressure2. Extremely low temperature

Van der Waals Equation

• a and b are constants specific to each gas. One corrects for the volume of the molecules, the other corrects for intermolecular forces of attraction. Which is which?

• B corrects for molecular volume• A corrects for attractive forces

Stoichiometry (revisited!)…• Objective: use known

information about part of a chemical equation to determine quantities of another part of the equation.

• Three step problem:

1. Convert to mols2. Mol to mol ratio3. Convert out of mols

• Conversions:

– g and mol, use Molar Mass– L and mol, use 22.4L

• Example –

– Given 25 L of oxygen gas, A)How many grams of water

can be produced?B)How many liters of

hydrogen will be required?

Gas Stoichiometry at non-STP

• Iron (III) chlorate decomposes with heat into iron (III) chloride and oxygen gas. If 37.6 liters of oxygen gas is collected at 800 torr and 30ºC, how many grams of iron (III) chlorate were decomposed?

• (108 g)

• Hydrogen peroxide decomposes in the presence of light into oxygen gas and liquid water. The bottle of “peroxide” which you buy at the drug store is really only 3.00% hydrogen peroxide and 97.0% water. If you poured a 1.00 pound bottle of 3.00% H

2O

2 into a dish and

allowed it to decompose, what would be the volume of just the oxygen gas if it were collected at 10ºC and with a combined pressure of 650 torr, assuming that all of the hydrogen peroxide decomposed?

Hint:

• (remember that the oxygen is being collected “over water” since it is bubbling out of the 97% water in the bottle). Vapor pressure of water at 10º C is 9.2 torr.

• (5.52 liters)

• 6.00 grams of solid magnesium react with 100 grams of hydrochloric acid which is 84% water. How many liters of hydrogen gas can be collected at 700 torr and 50oC? (Hint: the hydrogen is being collected “over water” since there is water in the hydrochloric acid solution which the hydrogen gas bubbles through as it is formed). The vapor pressure of water at 50oC is 92.5 torr.

• (7.27 liters)• Which reactant is left over and how

much? • (0.74 grams of magnesium)