A gas mixture contains each of the following gases at the indicated partial pressures: N₂, 215 torr; O₂, 102 torr; and He, 117 torr. What is the total pressure of the mixture? What mass of each gas is present in a 1.35-L sample of this mixture at 25.0 °C?

검증된 단계별 안내

Calculate the total pressure of the gas mixture by summing the partial pressures of each gas: \( P_{\text{total}} = P_{\text{N}_2} + P_{\text{O}_2} + P_{\text{He}} \).

Convert the temperature from Celsius to Kelvin using the formula: \( T(K) = T(°C) + 273.15 \).

Use the ideal gas law \( PV = nRT \) to find the number of moles of each gas. Rearrange the formula to solve for \( n \): \( n = \frac{PV}{RT} \).

Calculate the number of moles for each gas using their respective partial pressures, the volume of the container, and the temperature in Kelvin. Use the ideal gas constant \( R = 0.0821 \text{ L atm mol}^{-1} \text{ K}^{-1} \).

Convert the moles of each gas to mass using their molar masses: \( \text{mass} = n \times \text{molar mass} \). For \( \text{N}_2 \), \( \text{O}_2 \), and \( \text{He} \), use their respective molar masses.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Dalton's Law of Partial Pressures

Dalton's Law states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of each individual gas. This principle allows us to calculate the total pressure by simply adding the partial pressures of the gases present in the mixture.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for calculating the mass of each gas in the mixture, as it allows us to determine the number of moles from the known conditions of pressure, volume, and temperature.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). Knowing the molar mass of each gas in the mixture is crucial for converting the number of moles calculated from the Ideal Gas Law into mass, enabling us to find the mass of each gas present in the sample.

A gas mixture contains each of the following gases at the indicated partial pressures: N2, 215 torr; O2, 102 torr; and He, 117 torr. What is the total pressure of the mixture? What mass of each gas is present in a 1.35-L sample of this mixture at 25.0 °C?