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Chapter 5: Problem 80

A mixture of \(1.00 \mathrm{~g} \mathrm{H}_{2}\) and \(1.00 \mathrm{~g}\) He is placed in a \(1.00-\mathrm{L}\) container at \(27^{\circ} \mathrm{C}\). Calculate the partial pressure of each gas and the total pressure.

Short Answer

Expert verified
The partial pressure of hydrogen gas (H₂) is \(12.16 \mathrm{~atm}\), partial pressure of helium gas (He) is \(6.144 \mathrm{~atm}\), and the total pressure of the mixture is \(18.30 \mathrm{~atm}\).

Step by step solution

01

Identify relevant information

Given: Mass of hydrogen (H₂) = 1.00 g Mass of helium (He) = 1.00 g Volume of the container (V) = 1.00 L Temperature (T) = 27°C Note: Temperature must be converted to Kelvin (K) for calculations. So, T = 27 + 273.15 = 300.15 K.
02

Calculate the moles of each gas in the mixture

To calculate the moles of each gas, we'll use the molar mass of each element. Molar mass of hydrogen (H₂) = 2.016 g/mol Molar mass of helium (He) = 4.0026 g/mol Moles of H₂ (n_H₂) = mass_H₂ / molar_mass_H₂ = (1.00 g) / (2.016 g/mol) = 0.496 moles Moles of He (n_He) = mass_He / molar_mass_He = (1.00 g) / (4.0026 g/mol) = 0.250 moles
03

Apply the Ideal Gas Law for each gas in the mixture

The Ideal Gas Law formula is: PV = nRT, where P is pressure, V is volume, n is moles, R is the gas constant, and T is temperature. We will use the formula to find the partial pressure of each gas in the mixture. For hydrogen (H₂): P_H₂ = (n_H₂ * R * T) / V For helium (He): P_He = (n_He * R * T) / V Note: The gas constant R = 0.0821 L atm / K mol
04

Calculate partial pressures of each gas

Using the Ideal Gas Law, we can determine the partial pressures of each gas. For hydrogen (H₂): P_H₂ = (0.496 moles * 0.0821 L atm / K mol * 300.15 K) / 1.00 L = 12.16 atm For helium (He): P_He = (0.250 moles * 0.0821 L atm / K mol * 300.15 K) / 1.00 L = 6.144 atm
05

Calculate the total pressure of the mixture

The total pressure is the sum of the partial pressures of each individual gas in the mixture. Total Pressure (P_total) = P_H₂ + P_He = 12.16 atm + 6.144 atm = 18.30 atm The partial pressure of hydrogen gas is 12.16 atm, partial pressure of helium gas is 6.144 atm, and the total pressure of the mixture is 18.30 atm.

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