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Chapter 10: Problem 72

(a) What are the mole fractions of each component in a mixture of 15.08 \(\mathrm{g}\) of \(\mathrm{O}_{2}, 8.17 \mathrm{g}\) of \(\mathrm{N}_{2},\) and 2.64 \(\mathrm{g}\) of \(\mathrm{H}_{2}\) ? (b) What is the partial pressure in atm of each component of this mixture if it is held in a \(15.50-\mathrm{L}\) vessel at \(15^{\circ} \mathrm{C} ?\)

Short Answer

Expert verified
(a) The mole fractions of O₂, N₂, and H₂ are approximately 0.226, 0.140, and 0.634, respectively. (b) The partial pressures of O₂, N₂, and H₂ in the mixture are approximately 0.576 atm, 0.357 atm, and 1.617 atm, respectively.

Step by step solution

01

Calculate moles of each component

First, we need to convert grams to moles for each component using their molar masses: - O₂: Molar mass = 32 g/mol, so moles = 15.08 g / 32 g/mol ≈ 0.471 moles - N₂: Molar mass = 28 g/mol, so moles = 8.17 g / 28 g/mol ≈ 0.292 moles - H₂: Molar mass = 2 g/mol, so moles = 2.64 g / 2 g/mol = 1.32 moles
02

Calculate total moles

Add the moles of each component to find the total molesia: Total moles = moles of O₂ + moles of N₂ + moles of H₂ Total moles = 0.471 + 0.292 + 1.32 ≈ 2.083 moles
03

Determine the mole fractions

Now, we will calculate the mole fraction of each component by dividing their individual moles by the total moles: - Mole Fraction of O₂ = moles of O₂ / Total moles = 0.471 / 2.083 ≈ 0.226 - Mole Fraction of N₂ = moles of N₂ / Total moles = 0.292 / 2.083 ≈ 0.140 - Mole Fraction of H₂ = moles of H₂ / Total moles = 1.32 / 2.083 ≈ 0.634
04

Calculate the total pressure

First, we must convert the temperature from Celsius to Kelvin: Temperature = 15°C + 273.15 = 288.15 K Now, we'll use the Ideal Gas Law (PV = nRT) to find the total pressure. In this case, we have: - n (number of moles) = 2.083 mol - R (gas constant) = 0.0821 L atm/mol K - T (temperature) = 288.15 K - V (volume) = 15.50 L Solving for P (pressure): P = (nRT) / V P = (2.083 mol * 0.0821 L atm/mol K * 288.15 K) / 15.5 L P ≈ 2.55 atm
05

Calculate partial pressures

Finally, we'll find the partial pressures of each component by multiplying their mole fractions by the total pressure: - Partial Pressure of O₂ = Mole Fraction of O₂ * Total Pressure = 0.226 * 2.55 atm ≈ 0.576 atm - Partial Pressure of N₂ = Mole Fraction of N₂ * Total Pressure = 0.140 * 2.55 atm ≈ 0.357 atm - Partial Pressure of H₂ = Mole Fraction of H₂ * Total Pressure = 0.634 * 2.55 atm ≈ 1.617 atm So, the partial pressures of O₂, N₂, and H₂ in the mixture are 0.576 atm, 0.357 atm, and 1.617 atm, respectively.

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