Ideal Gas Law

1. Avogadro’s Principle

How much volume will one mole of hydrogen, oxygen, and helium occupy at STP?

Using the molar mass and gas density at STP :

H2 : H2

O2 : O2

He : He

2x16.0g1mole

cm3

0.001429gmLcm3

L1000mL 22.4L

mole

2x1.00794g1mole

cm3

0.0000899gmLcm3

L1000mL 22.4L

mole

1x4.0g1mole

cm3

0.00017847gmLcm3

L1000mL 22.4L

mole

It appears that :1 mole of a gas, at STP occupies 22.4 LSTP – standard temperature and pressureSTP - 0ºC, 101.3 kPa (1 atm, 760 mmHg)6.02 x 1023 gas particles, at STP, 22.4 L

Avogadro’s Principle – At equal temperature and pressure, equal volumes of gases contain equal number of molecules.

= constant V = volume, n = molesn

V

Moles ↑ Volume ↑ Direct Relationship Moles ↓ Volume ↓ A relationship between the number of particles

and the volume NOT a relationship between mass and volume!

H2 1 mole 2.016 g 22.4 L 0°C, 1 Atm

O2 1 mole 32.0 g 22.4 L 0°C, 1 Atm

He 1 mole 4.0 g 22.4 L 0°C, 1 Atm

DifferentGases

Same Numberof particles

DifferentMasses

SameVolume

Same Temperature

Pressure

Molar Volume – the volume of 1 mole of a gas, at a specified temperature and pressure.

Molar volume at STP, is 22.4 liters.

1 mole H2, at STP, occupies 22.4 L

1 mole O2, at STP, occupies 22.4 L

1 mole CO2, at STP, occupies 22.4 L

2. Ideal Gas Law Avogadro’s Principle : = constant

V = volume n = moles

Combined Gas Law :

Ideal Gas Law :

or PV = nRT Where R = Ideal Gas Constant

constantT

PV

constantTn

PV

n

V

PV = nRTP = pressure, kilopascals, kPaV = volume, Liters, Ln = number of moles

(convert grams to moles using Molar Mass)T = temperature, kelvin, K

R = Ideal Gas Constant,

Convert all units to the above, and you will only have to memorize one ideal gas constant!

Kmole

LkPa8.314

Calculate the ideal gas constant for STP, 1 mole of gas, and 22.4 liters!

PV=nRT (101.3 kPa)(22.4L) = (1mole)(R)(273K)

= R

R =

3K)(1mole)(27

(22.4L)(101.3kPa)

Kmole

LkPa8.314

3. Ideal and Real Gases

What volume does 3.5 moles of nitrogen gas occupy at STP?

How many grams of hydrogen gas are in 9.0 L at STP?

What volume will 125 g of carbon dioxide occupy at STP?

What is the volume (in liters) of 2.00 g CS2 vapor at 276 mm Hg and 70°C?

How many grams are in a sample of ammonia gas at 786 mm Hg, 2.5 L, and 28°C?

What pressure, in kPa, is exerted by 1.75 g of hydrogen gas in a 4.08 liter container at 35°C?

What is the volume of a gas that is 0.023 mole of nitrogen gas at STP?

How many moles of air are in a 6.0 L tire at STP?

How many moles of oxygen are in a 5.5 L canister at STP?

What mass of helium is in a 2.00 L balloon at STP?

Calculate the number of moles of gas that occupy a 3.45 L container at a pressure of 150 kPa and a temperature of 45.6°C.

What is the pressure in mmHg that a 0.44 g sample of carbon dioxide gas will exert at a temperature of 46.2°C when it occupies a volume of 5.00 L?

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

5. Density of a Gas Density = PV = nRT

so Density =

volumemass

Vn

RTP

volumemoles

Vn

Litersgrams

molegrams

xLitersmoles

MassMolarxRTP

What is the density of ammonia gas if the pressure is 700.0 mmHg and the temperature is 63.0°C?

What is the density of sulfur dioxide at STP?

What is the density of carbon dioxide at 26.0°C and 1.15 atm?

6. Molar Mass of Gases Molar mass =

Used to identify a gas. PV=nRT Solve for moles (n) from given pressure, volume,

and temperature. Divide given grams by calculated moles (n).

molegrams

What is the molar mass of a 1.25 g sample of gas with a volume of 1.00 L, at 730.0 mmHg, and 27.0°C?

What is the molar mass of 0.427 g of a gas that occupies 125 mL at STP?

What is the molar mass of a sample of gas that has a density of 0.285 g/L at 101 kPa and 29°C?

What is the molar mass of a gas if 142 g of the gas occupies a volume of 45.1 L at 28.4°C and 94.6 kPa?

7. Gas Stoichiometry

2 H2(g) + O2(g) 2 H2O(g)

2 molecules H2 + 1 molecule O2 2 molecules H2O

2 moles H2 + 1 mole O2 2 moles H2O at STP 2(22.4 L) H2 + 1(22.4 L) O2 2 (22.4 L) H2O

2 volumes H2 + 1 volume O2 2 volumes H2O At constant pressure and temperature, the

volumes of gaseous reactants and gaseous products can be expressed as ratios of small whole numbers.

At constant pressure and temperature, the mole ratio is equal to the volume ratio.

Calculating volumes of gases in chemical reactions:

1. Write a balanced chemical equation.

2. If the temperature and pressure remains constant during the chemical reaction, use the volume ratio.

3. Remember at STP, 1 mole of any gas occupies 22.4L.

If you are dealing with chemical reactions where:

Mixture of solids, liquids, and gases Change in temperature and/or pressure for

gases You will have to use the Ideal Gas Law.

1. Write a balanced chemical equation.

2. Calculate moles of gas from PV=nRT

3. Use mole ratio.

4. Convert moles of product to volume using PV=nRT.

Reactant A(gas) + B Product C + Product D(solid)

gas = P, V, T

moles A

PV=nRT

mass, grams

MM D

AmolesDmoles

moles D

Reactant A(gas) + B Product C(solid) + Product D(gas)

gas = P, V, T

moles A

PV=nRT

gas, P, V, T

PV=nRT

AmolesDmoles

moles D

If I have 27.0 L of hydrogen gas that reacts with an excess amount of nitrogen gas, how many liters of ammonia will be produced at the same temperature and pressure?

How many liters of carbon monoxide, at 27.0°C and 25.0 kPa can be produced from burning 65.5 g of carbon?

What volume of oxygen can be collected at 100.0  kPa and 25°C when 30.6 g KClO3 decomposes?

What volume of bromine gas (at 0.00°C, 98.0 kPa) is produced when 95.0 L of chlorine (at 50.0°C, 50.5 kPa) react with excess HBr?

Calculate the mass of hydrogen peroxide needed to obtain 0.460 L of oxygen gas at STP.

Magnesium metal will “burn” in carbon dioxide to produce elemental carbon and magnesium oxide. What mass of magnesium will “burn” in a 255 mL container of CO2 at 77.0°C and 65.0 kPa?