Ideal Gas Law & Gas Stoichiometry

Ideal Gas Law

P V = n R TP V = n R T• P = Pressure (atm)• V = Volume (L)• T = Temperature (K)• n = number of moles• R is a constant, called the Ideal Gas Constant• Instead of learning a different value for R for

all the possible unit combinations, we can just memorize one value and convert the units to match R.

• R = 0.0821 L atm / mol K

PV = nRTPV = nRT

• Calculate the number of moles of a gas contained in a 3.0 L vessel at 300.0K with a pressure of 1.50 atm

PV = nRTPV = nRT

• n = ?• V = 3.0 L• T = 300.0 K• P = 1.50 atm• PV = nRT• (1.50 atm)(3.0 L) = n (0.0821L atm / mol K)(300.0 K)

• n = 0.18 mol

Example

Dinitrogen monoxide (N2O), laughing gas, is used by dentists as an anesthetic. If 2.86 mol of gas occupies a 20.0 L tank at 23°C, what is the pressure (mmHg) in the tank in the dentist office?

Note: 1atm = 760 mm Hg

Avogadro’s Principle

• Avogadro’s Principle – equal volumes of gases at equal temperature and pressure contain the same number of particles

• Molar volume – the volume of gas that 1 mole of a substance occupies at STP

• At STP 1 mol of a gas = 22.4 L• New conversion factor at STP ONLY!

1 mol22.4 L

Example

• Calculate the volume 0.881 mol of a gas will occupy at STP.

• 0.881 mol x 22.4 L = 19.7 L 1 mol(You could also have worked this out with

the ideal gas law equation)

Example

• Calculate the volume that 2.000 kg of methane would occupy at STP.

• 2.000 kg x 1x10 3g x 1 mol x 22.4 L = 1kg 16.05g 1 mol• 2791 L CH4

Gas Stoichiometry Rules

• Balance the equation.• STARTING IN VOLUME:

– Use the ideal gas law to find moles of the gas. – Use the molar ratio. – Convert from moles to what you want.

• STARTING IN MOLES:– Use the molar ratio.– Use the ideal gas law to convert from moles to

volume.

Problem #1

• How many grams of copper (II) carbonate are required to produce 11.2 dm3 of carbon dioxide at 22.3° C and standard pressure?

• 57.1 g CuCO3

Problem #2

• How many grams of potassium chlorate are required to produce 22.40 liters of oxygen at 25.00° C and 202.6 kPa?

• 149.7 g KClO3

Problem #3

• How many grams of water are produced with 10.0 dm3 of carbon dioxide at 273° C and standard pressure by the combustion of ethane?

• 6.0 g H2O

Problem #4• How many grams of magnesium are

required to react with hydrochloric acid to produce 0.50 dm3 of hydrogen at 21° C and standard pressure?

• 0.50 g Mg

Problem #5

• How many grams of sodium are required to react with water to produce 2.40 dm3 of hydrogen at 25° C and standard pressure?

• 4.6 g Na