Textbook Question
What is the mole fraction of each gas in the mixture described in Problem 10.83?
Ch.10 - Gases: Their Properties & Behavior
Chapter 10, Problem 86b
A mixture of 14.2 g of H2 and 36.7 g of Ar is placed in a 100.0-L container at 290 K. (b) What is the partial pressure of Ar in atmospheres?
Verified step by step guidance1
insert step 1: Identify the relevant gas law for calculating partial pressure, which is Dalton's Law of Partial Pressures. This law states that the total pressure of a gas mixture is the sum of the partial pressures of each individual gas.
insert step 2: Calculate the number of moles of Ar using its molar mass. The molar mass of Ar (Argon) is approximately 39.95 g/mol. Use the formula: \( n = \frac{\text{mass}}{\text{molar mass}} \).
insert step 3: Use the ideal gas law to find the partial pressure of Ar. The ideal gas law is given by \( PV = nRT \), where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the ideal gas constant (0.0821 L·atm/mol·K), and \( T \) is the temperature in Kelvin.
insert step 4: Rearrange the ideal gas law to solve for the partial pressure of Ar: \( P = \frac{nRT}{V} \).
insert step 5: Substitute the known values (\( n \) from step 2, \( R = 0.0821 \) L·atm/mol·K, \( T = 290 \) K, and \( V = 100.0 \) L) into the equation from step 4 to calculate the partial pressure of Ar.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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 fundamental in calculating the behavior of gases under various conditions, allowing us to determine properties like pressure when the amount of gas and temperature are known.
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Ideal Gas Law Formula
Partial Pressure
Partial pressure is the pressure that a single gas in a mixture would exert if it occupied the entire volume alone. According to Dalton's Law of Partial Pressures, the total pressure of a gas mixture is the sum of the partial pressures of each individual gas, which is crucial for calculating the pressure of argon in this scenario.
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Molar Mass and Moles Calculation
To find the partial pressure of argon, we first need to calculate the number of moles of each gas using their molar masses. The molar mass of H2 is approximately 2 g/mol, and for Ar, it is about 40 g/mol. This step is essential for applying the Ideal Gas Law and determining the contribution of argon to the total pressure in the container.
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Related Practice
Textbook Question
A mixture of 14.2 g of H2 and 36.7 g of Ar is placed in a 100.0-L container at 290 K. (a) What is the partial pressure of H2 in atmospheres?
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Textbook Question
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