Calculating Partial Pressure Of Hydrogen In A Gas Mixture A Chemistry Guide

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In the realm of chemistry, understanding the behavior of gases is crucial. Gases, unlike solids and liquids, are highly compressible and readily mix with each other. This mixing leads to the concept of partial pressure, which is the pressure exerted by an individual gas in a mixture of gases. This article delves into the calculation of the partial pressure of hydrogen gas within a container holding a mixture of gases. We'll explore the fundamental principles behind partial pressures and apply them to a specific scenario involving a container with a known amount of gas, where hydrogen constitutes a certain percentage of the total moles, and the total pressure is given.

At the heart of this calculation lies Dalton's Law of Partial Pressures. This law, a cornerstone of gas behavior, states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of each individual gas in the mixture. In simpler terms, each gas contributes to the overall pressure as if it were the only gas present. The partial pressure of a gas is directly proportional to its mole fraction in the mixture. The mole fraction represents the ratio of the number of moles of a particular gas to the total number of moles of all gases in the mixture. This relationship provides a powerful tool for determining the contribution of each gas to the total pressure.

Applying the Formula

The formula provided, $ \frac{P_a}{P_T} = \frac{n_a}{n_T} $, mathematically expresses Dalton's Law of Partial Pressures. Let's break down each component: $ P_a $ represents the partial pressure of gas "a", which in our case is hydrogen. This is the value we aim to calculate. $ P_T $ signifies the total pressure of the gas mixture, a known quantity in our scenario. $ n_a $ denotes the number of moles of gas "a" (hydrogen), which we can determine from the given percentage. Finally, $ n_T $ represents the total number of moles of gas in the container, also provided in the problem statement. By plugging in the known values and rearranging the formula, we can isolate and calculate the partial pressure of hydrogen.

Consider a scenario where a container holds a total of 6.4 moles of gas. Within this mixture, hydrogen gas comprises 25% of the total moles. The total pressure exerted by the gas mixture is measured to be 1.24 atm. Our objective is to determine the partial pressure of hydrogen gas within this container. This problem provides a practical application of Dalton's Law of Partial Pressures, allowing us to calculate the contribution of hydrogen to the overall pressure.

Let's walk through the solution methodically, applying the formula and the information provided:

  1. Identify the knowns:

    • Total moles of gas ( $ n_T $ ) = 6.4 moles
    • Percentage of hydrogen gas = 25%
    • Total pressure ( $ P_T $ ) = 1.24 atm

  2. Calculate the moles of hydrogen gas ( $ n_a $ ):

    Since hydrogen constitutes 25% of the total moles, we can calculate the moles of hydrogen as follows:

    na=0.25∗nT=0.25∗6.4 moles=1.6 moles n_a = 0.25 * n_T = 0.25 * 6.4 \text{ moles} = 1.6 \text{ moles}

    This calculation determines the amount of hydrogen present in the mixture, a crucial value for determining its partial pressure.

  3. Apply the formula:

    Using the formula $ \frac{P_a}{P_T} = \frac{n_a}{n_T} $, we can plug in the known values:

    Pa1.24 atm=1.6 moles6.4 moles \frac{P_a}{1.24 \text{ atm}} = \frac{1.6 \text{ moles}}{6.4 \text{ moles}}

    This sets up the equation to solve for the partial pressure of hydrogen.

  4. Solve for the partial pressure of hydrogen ( $ P_a $ ):

    Rearranging the equation to isolate $ P_a $, we get:

    Pa=1.6 moles6.4 moles∗1.24 atm P_a = \frac{1.6 \text{ moles}}{6.4 \text{ moles}} * 1.24 \text{ atm}

    Pa=0.31 atm P_a = 0.31 \text{ atm}

    This final calculation yields the partial pressure of hydrogen gas in the container.

Therefore, the partial pressure of hydrogen gas in the container is 0.31 atm. This result highlights the application of Dalton's Law of Partial Pressures in determining the individual contributions of gases within a mixture. Understanding partial pressures is fundamental in various chemical contexts, including gas reactions, atmospheric studies, and industrial processes. By applying the formula and understanding the underlying principles, we can effectively analyze and predict the behavior of gases in mixtures. This calculation demonstrates how the mole fraction of a gas directly influences its partial pressure, a key concept in understanding gas behavior.

This detailed solution provides a clear understanding of how to calculate the partial pressure of a gas in a mixture, emphasizing the importance of Dalton's Law of Partial Pressures and its applications in chemistry. The step-by-step approach ensures clarity and allows for easy replication of the calculation in similar scenarios. In conclusion, the partial pressure of hydrogen in the given mixture is 0.31 atm, a value derived from the principles of gas behavior and stoichiometry.