12.1 The Ideal Gas Law Ms. Munir

The Molar Volume of Gases Law of combining volumes: When gases react, the volumes of the reactants and the products, measured at equal temperatures and pressures, are always in whole number ratios. (Gay-Lussac) 2 volumes of hydrogen gas react with 1 volume of oxygen gas to produce 2 volumes of water vapour.

Continued… Law of multiple proportions: The masses of the elements that combine can be expressed in small whole number ratios. (Dalton) Avogadro’s hypothesis: Equal volumes of all ideal gases at the same temperature and pressure contain the same number of molecules.

Picture this!

Avogadro’s Law n α V or n = kV or n = number of moles V = volume k = a constant

Molar Volume Molar volume is measured in units of L/mol. You can find the molar volume of a gas by dividing its volume by the number of moles that are present (V/n).

Example 1 A resealable 1.30 L container has a mass of 4.73 g. Nitrogen gas, N2(g), is added to the container until the pressure is 98.0 kPa at 22.0°C. Together, the container and the gas have a mass of 6.18 g. Calculate the molar volume of nitrogen gas at STP.

Solution

Solution continued…

Memorize! The molar volume of an ideal gas at STP is 22.4 L/mol.

Example 2 What is the volume of 3.0 mol of nitrous oxide, NO2(g), at STP? ni = 1.0 mol Vi = 22.4 L nf = 3.0 mol of NO2 Therefore, there are 67 L of nitrous oxide

Example 3 Suppose that you have 44.8 L of methane gas at STP. How many moles are present? What is the mass (in g) of the gas? How many molecules of gas are present?

Solution

Please note! Although the volumes of all gases are the same at STP (22.4L), one mole of a gas will have a different mass and density than one mole of another gas.

Ideal Gas Law

Value of R

Ideal Gas Law The ideal gas law states that the pressure multiplied by the volume is equal to the number of moles multiplied by the universal gas constant and the temperature. PV = nRT Guidelines for Using the Ideal Gas Law: Always convert the temperature to kelvins (K). Always convert the masses to moles (mol). Always convert the volumes to litres (L). Always convert the pressures to kilopascals (kPa). Value of R (8.314 kPa·L/mol·K)

Example 4 Use the ideal gas law to calculate the molar volume of a gas at standard ambient temperature and pressure (SATP). The conditions for SATP are 298 K and 100 kPa.

Solution Given: PV = nRT P = 100 kPa n = 1.00 mol R = 8.314 kPa·L/mol·K T = 298 K PV = nRT V = (1.00mol x 8.314kPa.L/mol.K x 298K)/100kPa = 24.8L The molar volume of a gas at SATP is 24.8L/mol.

Example 5 A cylinder of laughing gas (N2O) has a diameter of 23.0 cm and a height of 140 cm. The pressure is 108 kPa, and the temperature is 294 K. How many grams of laughing gas are in the cylinder?

Solution V = πr2h = π × 11.52 cm2 × 140 cm = 5.73 × 104 cm3 = 57.3 L P = 108 kPa V = πr2h, where r = 11.5 cm and h = 140 cm R = 8.314 kPa·L/mol·K T = 294 K V = πr2h = π × 11.52 cm2 × 140 cm = 5.73 × 104 cm3 = 57.3 L PV = nRT n = (108kPa x 57.3L)/(8.314kPa.L/mol.K x 294K) n = 2.53mol MN2O = 44.02 g/mol m = n × M = 2.53 mol × 44.02 g/mol = 111g Therefore, 111 g of laughing gas is in the cylinder.

Work! P 488 # 1 – 7 McGrawHill P 581 # 1 – 4; p 589 # 1 – 6 Nelson