Question

A twenty-eight-liter volume of gas contains 11 g methane, 1.5-gram nitrogen and 16-gram carbon dioxide. Determine partial pressure of each gas.

Answer 1

Based on Dalton's Law, for a mixture of gases, the total pressure is the sum of the partial pressure of each gas.

Partial pressure (p) of each gas is related to the total pressure (P) as follows:

p = X * P----------(1)

where X is the mole fraction of that gas

X = moles of a particular gas/total number of moles of all gases in the mixture--------------(2)

Step 1: Calculate the moles of each gas

Mass of methane, CH4 = 11 g

Mass of nitrogen, N2 = 1.4 g

Mass of carbon dioxide, CO2 = 16 g

# moles of CH4 = 11 g/16 gmol-1 = 0.6875

# moles of N2 = 1.4/28 = 0.05

# moles of CO2 = 16/44 = 0.3636

Total moles = 0.6875+0.05+0.3636 = 1.1011

Step2: Calculate mole fractions of each gas

Based on equation (2)

X(CH4) = 0.6875/1.1011 = 0.6244

X(N2) = 0.05/1.1011 = 0.0454

X(CO2) = 0.3636/1.1011 = 0.3302

Step 3: Calculate the total pressure

Based on ideal gas equation:

PV = nRT

given that;

V = 28 L

n = total moles = 1.1011

R = gas constant = 0.0821 Latm/mol-K

Since temp T is not given, let us consider room temperature of 25 C = 25 + 273 = 298 K

Now, P = nRT/V = 1.011*0.0821*298/28 = 0.962 atm

Step 3: Calculate partial pressures

Based on equation:

p(CH4) = 0.6244*0.962 atm = 0.601 atm

P(N2) = 0.0454*0.962 atm = 0.044 atm

P(CO2) = 0.3302*0.962 atm = 0.318 atm