Chapter 11 – Molecular Composition of Gases

11-1 Volume-Mass Relationships of Gases  Joseph Gay-Lussac, French chemist in the 1800s, found that at constant temperature and pressure, the volumes of gaseous reactants and products can be expressed as ratios of small whole numbers.  This is called Gay-Lussac’s law of combining volumes of gases.  Today we know that these volume relationships are given by the coefficients of a balanced chemical equation and are equivalent to the mole ratios of gaseous reactant and products.

1-1 Gay-Lussac’s Law of Combining Volumes  hydrogen + oxygen  water vapor  hydrogen + chlorine  hydrogen chloride

11-1 Volume-Mass Relationships of Gases  In 1811, Amedeo Avogadro proposed that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.  This is known as Avogadro’s law.

11-1 Avogadro’s Law  H 2 (g) + Cl 2 (g)  2HCl(g)  One volume of hydrogen combines with one volume of chlorine to form two volumes of hydrogen chloride.  One molecule of hydrogen combines with one molecule of chlorine to form two molecules of hydrogen chloride.

11-1 Avogadro’s Law  Gas volume (V) is directly proportional to the number of particles (n) at constant temperature and pressure. V = kn or k = V/n k = V/n

11-1 Molar Volume of Gases  One mole of any gas will occupy the same volume as any other gas at the same temperature and pressure, regardless of the mass of the particle.  The volume occupied by one mole of any gas at STP is called the standard molar volume of a gas and is equal to 22.4 L/mol.

11-1 Molar Volume of Gases  A sample of hydrogen gas occupies 14.1 L at STP. How many moles of the gas are present?  At STP, a sample of neon gas occupies 0.55 L. How many moles of neon gas does this represent?

11-2 The Ideal Gas Law  To describe a gas sample, four quantities are needed: pressure, volume, temperature, and number of moles  V α 1/P (Boyle’s Law)  V α T (Charles’ Law)  V α n (Avogadro’s Law)  V α 1/P x T x n  V = R x 1/P x T x n  PV = nRT  R is the gas constant. P is pressure in atm or kPa V is volume in L (dm 3 ) N is moles T is temp in Kelvin

11-2 The Value of R  Remember, one mole of any gas at STP has a volume of 22.4 L. We can use this definition to determine the value of R.  If pressure is in atm…  If pressure is in kPa…  Remember, 1 L = 1 dm 3

11-2 The Ideal Gas Law  The ideal gas law is the mathematical relationship among pressure, volume, temperature and the number of moles of a gas.  PV = nRT P – pressure (atm or kPa) V – volume (L) n – moles R – gas constant ( L.atm/mol.K or 8.31 L.kPa/mol.K) T – temperature (K)

11-2 Ideal Gas Law  What volume will be occupied by 0.21 moles of oxygen gas at 25°C and 1.05 atm of pressure?

11-2 Ideal Gas Law  A sample of carbon dioxide gas has a mass of 1.20 g at 25°C and 1.05 atm. What volume does this gas occupy?

11-2 The Ideal Gas Law  Variations: n = m/MM so PV = mRT/MM so PV = mRT/MM and MM = mRT/PV D = m/V so D = MMP/RT

11-2 The Ideal Gas Law  What is the molar mass of a gas if g of the gas occupies a volume of 125 mL at 20.0°C and atm?

11-2 The Ideal Gas Law  What is the density of argon gas, Ar, at a pressure of 551 torr and a temperature of 25°C?

11-3 Stoichiometry of Gases  Volume-Volume calculations – just use the mole ratio! C 3 H 8 + 5O 2  3CO 2 + 4H 2 O  What volume, in L, of oxygen, is required for the complete combustion of L of propane?

11-4 Effusion and Diffusion  Diffusion – the gradual mixing of two gases due to their spontaneous, random motion.  Effusion – the process by which the molecules of a gas confined in a container randomly pass through a tiny opening in the container.

11-4 Effusion and Diffusion The rates of effusion and diffusion depend on the relative velocities of the gas molecules.  The velocity of a gas varies inversely with its mass. Lighter molecules move faster than heavier molecules at equivalent temperatures.

11-4 Effusion and Diffusion  Remember, temperature is a measure of average kinetic energy.  Particles of two gas samples (A and B) at the same temperature have the same average kinetic energy.  KE =1/2 mv 2  Graham’s Law of Effusion compares rates of effusion and diffusion for gases.  The relationship can be derived easily.

11-4 Effusion and Diffusion  The rate of effusion or diffusion for gases depends on the average velocities of the particles.  Graham’s Law of Effusion – For two gases, A and B, at the same temperature, the following relationship exists…

11-4 Effusion and Diffusion  Compare the rates of effusion of hydrogen and oxygen at the same temperature and pressure.

11-4 Effusion and Diffusion  If a molecule of neon gas travels at an average of 400 m/s at a given temperature, estimate the average speed of a molecule of butane gas, C 4 H 10, at the same temperature.