III. Ideal Gas Law (p , ) Ch. 10 & 11 - Gases

Quantities to Describe Gases b P: Pressure b V: Volume b T: Temperature (Kelvin!) b n: # of moles

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

PV T VnVn PV nT 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:

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

Ideal Gas Constant, R b We know that: 1 mol of a gas occupies 22.4 L at STP ( K and kPa) b R = PV = ( kPa)(22.4L) Tn(273.15K)(1mol) R = 8.31 L·kPa/mol·K

Ideal Gas Constant, R b Units of numerator depend on: Unit of volume and pressure Common units of R  Numerical Value Units 62.4L·mmHg mol·K L·atm mol·K 8.314J mol·K 8.314L·kPa mol·K

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 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 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

M from IGL b a) If the P, V, T, and mass are known for a gas sample, then n can be calculated using IGL b Then, the molar mass is found by dividing the mass by the number of moles

M from IGL b b) The number of moles (n) is equal to mass (m) divided by molar mass (M) g ÷ g = g x mol = mol mol g c) Substitute m/M for n in IGL: PV = mRT OR M = mRT M PV

D from IGL b Density, D, is m/V which results in: M = DRT P Rearranging for D: D = MP RT