I. The Gas Laws Ch Gases

A. Boyle’s Law b The pressure and volume of a gas are inversely related at constant mass & temp P V P 1 V 1 = P 2 V 2

A. Boyle’s Law

V T B. Charles’ Law b The volume and absolute temperature (K) of a gas are directly related at constant mass & pressure V 1 = V 2 T 1 T 2

B. Charles’ Law

V n A. Avogadro’s Principle b Equal volumes of gases contain equal numbers of moles at constant temp & pressure true for any gas V 1 = V 2 n 1 n 2

= kPV PTPT VTVT nT D. Combined Gas Law P1V1n1T1P1V1n1T1 = P2V2n2T2P2V2n2T2 P 1 V 1 T 2 n 2 = P 2 V 2 T 1 n 1

GIVEN: V 1 = 473 cm 3 T 1 = 36°C = 309K V 2 = ? T 2 = 94°C = 367K WORK: P 1 V 1 T 2 = P 2 V 2 T 1 E. Gas Law Problems b A gas occupies 473 cm 3 at 36°C. Find its volume at 94°C. CHARLES’ LAW TT VV (473 cm 3 )(367 K)=V 2 (309 K) V 2 = 562 cm 3

GIVEN: V 1 = 100. mL P 1 = 150. kPa V 2 = ? P 2 = 200. kPa WORK: P 1 V 1 T 2 = P 2 V 2 T 1 E. Gas Law Problems b A gas occupies 100. mL at 150. kPa. Find its volume at 200. kPa. BOYLE’S LAW PP VV (150.kPa)(100.mL)=(200.kPa)V 2 V 2 = 75.0 mL

GIVEN: V 1 = 2.00 L n 1 = 5.00 moles n 2 = 10.0 moles V2 = ?V2 = ? WORK: V 1 n 2 = V 2 n 1 (2.00 L)(10.0 moles) =(5.00 moles) V 2 V 2 = 4.00 L E. Gas Law Problems b A sample of gas occupies 2.00 L with 5.00 moles present. What would happen to the volume if the number of moles is increased to 10.0? V  n  AVOGADRO’S LAW

GIVEN: V 1 = 7.84 cm 3 P 1 = 71.8 kPa T 1 = 25°C = 298 K V2 = ?V2 = ? P 2 = kPa T 2 = 273 K WORK: P 1 V 1 T 2 = P 2 V 2 T 1 (71.8 kPa)(7.84 cm 3 )(273 K) =( kPa) V 2 (298 K) V 2 = 5.09 cm 3 E. Gas Law Problems b A gas occupies 7.84 cm 3 at 71.8 kPa & 25°C. Find its volume at STP. P  T  VV COMBINED GAS LAW

Ch Gases II. Two More Laws

B. Dalton’s Law b The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases. P total = P 1 + P When a H 2 gas is collected by water displacement, the gas in the collection bottle is actually a mixture of H 2 and water vapor.

GIVEN: P H2 = ? P total = 94.4 kPa P H2O = 2.72 kPa WORK: P total = P H2 + P H2O 94.4 kPa = P H kPa P H2 = 91.7 kPa B. Dalton’s Law b Hydrogen gas is collected over water at 22.5°C. Find the pressure of the dry gas if the atmospheric pressure is 94.4 kPa. Look up water-vapor pressure on p.899 for 22.5°C. Sig Figs: Round to least number of decimal places. The total pressure in the collection bottle is equal to atmospheric pressure and is a mixture of H 2 and water vapor.

GIVEN: P gas = ? P total = torr P H2O = 42.2 torr WORK: P total = P gas + P H2O torr = P H torr P gas = torr b A gas is collected over water at a temp of 35.0°C when the barometric pressure is torr. What is the partial pressure of the dry gas? Look up water-vapor pressure on p.899 for 35.0°C. Sig Figs: Round to least number of decimal places. B. Dalton’s Law The total pressure in the collection bottle is equal to barometric pressure and is a mixture of the “gas” and water vapor.

Ideal Gas Law Ch. 14 Gases

PV T VnVn PV nT A. Ideal Gas Law = k UNIVERSAL GAS CONSTANT R= L  atm/mol  K R=8.315 dm 3  kPa/mol  K = R You don’t need to memorize these values! Merge the Combined Gas Law with Avogadro’s Principle:

A. Ideal Gas Law UNIVERSAL GAS CONSTANT R= L  atm/mol  K R=8.315 dm 3  kPa/mol  K PV=nRT You don’t need to memorize these values!

GIVEN: P = ? atm n = mol T = 16°C = 289 K V = 3.25 L R = L  atm/mol  K WORK: PV = nRT P(3.25)=(0.412)(0.0821)(289) L mol L  atm/mol  K K P = 3.01 atm C. Ideal Gas Law Problems b Calculate the pressure in atmospheres of mol of He at 16°C & occupying 3.25 L.

GIVEN: V = ? n = 85 g T = 25°C = 298 K P = kPa R = dm 3  kPa/mol  K C. Ideal Gas Law Problems b Find the volume of 85 g of O 2 at 25°C and kPa. = 2.7 mol WORK: 85 g 1 mol = 2.7 mol g PV = nRT (104.5)V=(2.7) (8.315) (298) kPa mol dm 3  kPa/mol  K K V = 64 dm 3