A Gas Mixture Contains 20.0 G He Gas And 6.0 G Hydrogen Gas At A Total Pressure Of 800 Torr. What Is this mixture's molar composition, partial pressures, and other relevant properties? Understanding the behavior of gas mixtures is fundamental in chemistry and physics, especially for applications involving gas laws, mixtures, and partial pressures. This article explores how to analyze such a mixture systematically, calculating the number of moles, mole fractions, partial pressures, and related properties.
Understanding the Composition of the Gas Mixture
Before diving into calculations, it's crucial to interpret the given data correctly. The mixture contains helium (He) and hydrogen (H₂) gases, with specified masses and a total pressure. We will use this information to determine the number of moles of each gas, their mole fractions, and the partial pressures contributing to the total pressure.
Calculating Moles of Each Gas
The first step involves converting the given masses into moles, using the molar masses of helium and hydrogen.
Molar Mass of Helium (He)
- Atomic mass of He ≈ 4.00 g/mol
Molar Mass of Hydrogen (H₂)
- Molecular mass of H₂ ≈ 2.02 g/mol (since atomic hydrogen ≈ 1.008 g/mol, and H₂ is diatomic)
Number of Moles of Helium
\[ n_{He} = \frac{\text{mass of He}}{\text{molar mass of He}} = \frac{20.0\, \text{g}}{4.00\, \text{g/mol}} = 5.00\, \text{mol} \]Number of Moles of Hydrogen
\[ n{H2} = \frac{\text{mass of H}2}{\text{molar mass of H}2} = \frac{6.0\, \text{g}}{2.02\, \text{g/mol}} \approx 2.97\, \text{mol} \]Note: The slight approximation here is due to rounding.
Calculating Total Moles in the Mixture
The total number of moles in the mixture is simply the sum of the moles of each component:
\[
n{total} = n{He} + n{H2} = 5.00 + 2.97 \approx 7.97\, \text{mol}
\]
This total will be useful for calculating mole fractions and partial pressures.
Mole Fractions of Each Gas
Mole fraction (X) indicates the proportion of each gas in the mixture:
\[
X{He} = \frac{n{He}}{n_{total}} = \frac{5.00}{7.97} \approx 0.628
\]
\[
X{H2} = \frac{n{H2}}{n_{total}} = \frac{2.97}{7.97} \approx 0.373
\]
These fractions help determine each gas's contribution to the total pressure.
Calculating Partial Pressures
Dalton’s Law states that each gas in a mixture exerts a partial pressure proportional to its mole fraction:
\[
P{gas} = X{gas} \times P_{total}
\]
Given:
- Total pressure, \( P_{total} = 800\, \text{Torr} \)
Partial Pressure of Helium
\[
P{He} = X{He} \times P_{total} = 0.628 \times 800\, \text{Torr} \approx 502.4\, \text{Torr}
\]
Partial Pressure of Hydrogen
\[ P{H2} = X{H2} \times P_{total} = 0.373 \times 800\, \text{Torr} \approx 298.4\, \text{Torr} \]These partial pressures are crucial for understanding the behavior of each component within the mixture.
Additional Properties and Applications
Knowing the moles and partial pressures, several other properties and applications can be analyzed:
1. Gas Behavior and Ideal Gas Law
- The ideal gas law, \( PV = nRT \), can be used to determine the volume of the mixture at a given temperature.
- For example, assuming a temperature \( T \) (say, 298 K), the volume \( V \) can be calculated as:
2. Molar Ratios and Composition
- The molar ratio of He to H₂ is approximately 5.00:2.97, or about 1.68:1, which can be relevant in chemical reactions or processes where specific ratios are needed.
3. Applications in Industry and Research
- Gas mixtures like this are common in laboratories, welding (helium-hydrogen mixtures), and gas chromatography.
- Understanding partial pressures helps optimize conditions for reactions or processes like gas separation.
Summary of Key Calculations
- Helium moles: 5.00 mol
- Hydrogen moles: 2.97 mol
- Total moles: 7.97 mol
- Mole fraction of He: 0.628
- Mole fraction of H₂: 0.373
- Partial pressure of He: approximately 502.4 Torr
- Partial pressure of H₂: approximately 298.4 Torr
Conclusion
Analyzing a gas mixture involves converting given masses into moles, calculating mole fractions, and applying Dalton’s Law to find partial pressures. In this example, the mixture contains about 5.00 mol of helium and 2.97 mol of hydrogen, with partial pressures of approximately 502.4 Torr and 298.4 Torr, respectively. Such calculations are essential in various scientific and industrial applications, providing insight into the behavior and properties of gas mixtures under different conditions.
Understanding these principles allows chemists and engineers to design processes, interpret experimental data, and optimize conditions for reactions involving multiple gases. Whether in laboratory settings or large-scale industrial operations, mastery of gas mixture analysis remains a fundamental skill in the physical sciences.
