15. A mixture of carbon dioxide and hydrogen gases is maintained in a 9.62 L flask at a pressure of 3.44 atm and a temperature of 63 °C. If the gas mixture contains 12.5 grams of carbon dioxide, the number of grams of hydrogen in the mixture is
g.

Mass = 1.84 g

Explanation:

Given data:

Total pressure = 3.44 atm

Volume of flask = 9.62 L

Temperature = 63°C = 63+273.15K = 336.15 K

Mass of CO₂ = 12.5 g

Mass of hydrogen = ?

Solution:

Number of moles of CO₂:

Number of moles = mass/molar mass

Number of moles = 12.5 g/ 44 g/mol

Number of moles = 0.28 mol

Pressure of CO₂:

PV = nRT

R = general gas constant = 0.0821 atm.L/mol.K

P = 0.28 mol × 0.0821 atm.L/mol.K × 336.15 K / 9.62 L

P = 7.73 atm.L/ 9.62 L

P =  0.8 atm

Total pressure = Partial pressure of CO₂ + Partial pressure of H₂

3.44 atm = 0.8 atm + P(H₂)

P(H₂) = 3.44 atm - 0.8 atm

P(H₂) = 2.64 atm

Number of moles of hydrogen:

PV = nRT

2.64 atm  × 9.62 L = n × 0.0821 atm.L/mol.K × 336.15 K

25.39 atm.L = n × 27.59atm.L/mol

n = 25.39 atm.L / 27.59atm.L/mol

n = 0.92 mol

Mass of hydrogen:

Mass = number of moles × molar mass

Mass = 0.92 mol ×  2 g/mol

Mass = 1.84 g

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