Question

The molar analysis of a gas mixture at \(290 \mathrm{~K}\) and $250 \mathrm{kPa}\( is 65 percent \)\mathrm{N}_{2}, 20\( percent \)\mathrm{O}_{2}$, and 15 percent \(\mathrm{CO}_{2}\). Determine the mass fraction and partial pressure of each gas.

Short answer

Answer: The mass fractions and partial pressures of each gas are: - N2: mass fraction ≈ 0.593, partial pressure ≈ 162.5 kPa - O2: mass fraction ≈ 0.270, partial pressure ≈ 50 kPa - CO2: mass fraction ≈ 0.137, partial pressure ≈ 37.5 kPa

Step-by-step solution

Calculate the molar mass of each gas

To find the mass fractions, we need the molar mass of each gas. For N2, O2, and CO2, we can use the periodic table to determine their molar masses: - N2 has a molar mass of 28 g/mol - O2 has a molar mass of 32 g/mol - CO2 has a molar mass of 44 g/mol

Calculate the mass fraction of each gas

Mass fraction is the mass of each component divided by the total mass of the mixture. When given the molar analysis, we can calculate the mass fraction of each gas as follows: - N2 mass fraction = 0.65 x 28 / (0.65 x 28 + 0.20 x 32 + 0.15 x 44) - O2 mass fraction = 0.20 x 32 / (0.65 x 28 + 0.20 x 32 + 0.15 x 44) - CO2 mass fraction = 0.15 x 44 / (0.65 x 28 + 0.20 x 32 + 0.15 x 44) Calculate the mass fractions: - N2 mass fraction ≈ 0.593 - O2 mass fraction ≈ 0.270 - CO2 mass fraction ≈ 0.137

Calculate the partial pressure of each gas

The partial pressure of each gas can be found using Dalton's Law, which states that the partial pressure of a gas in a mixture is equal to the mole fraction of that gas times the total pressure. For N2, O2, and CO2, use their mole fractions (given as percentages) and the total pressure of 250 kPa: - N2 partial pressure = 0.65 x 250 kPa - O2 partial pressure = 0.20 x 250 kPa - CO2 partial pressure = 0.15 x 250 kPa Calculate the partial pressures: - N2 partial pressure ≈ 162.5 kPa - O2 partial pressure ≈ 50 kPa - CO2 partial pressure ≈ 37.5 kPa So, the mass fractions and partial pressures of each gas are: - N2: mass fraction ≈ 0.593, partial pressure ≈ 162.5 kPa - O2: mass fraction ≈ 0.270, partial pressure ≈ 50 kPa - CO2: mass fraction ≈ 0.137, partial pressure ≈ 37.5 kPa