Calculating Partial Pressure Of Hydrogen In Gas Mixture

In chemistry, understanding the behavior of gases is crucial, especially when dealing with mixtures. One fundamental concept is the partial pressure, which is the pressure exerted by an individual gas in a mixture of gases. This concept is particularly useful in various applications, such as determining gas concentrations in industrial processes, understanding respiratory physiology, and analyzing atmospheric composition. In this article, we will explore how to calculate the partial pressure of a gas within a mixture, focusing on a specific example involving hydrogen gas. We will delve into the principles behind the calculation and provide a step-by-step guide to solving the problem. The formula Pₑ/Pₜ = nₑ/nₜ serves as the cornerstone for calculating partial pressures, where Pₑ represents the partial pressure of a specific gas, Pₜ signifies the total pressure of the mixture, nₑ denotes the number of moles of the specific gas, and nₜ indicates the total number of moles of gas in the mixture. This relationship underscores the direct proportionality between a gas's partial pressure and its molar fraction within the mixture. Mastering this calculation is essential for anyone studying chemistry, as it forms the basis for understanding more complex gas behavior and reactions. By the end of this article, you will be equipped with the knowledge and skills to confidently calculate the partial pressure of hydrogen, or any other gas, in a mixture.

Consider a scenario where a container holds 6.4 moles of gas in total. Within this mixture, hydrogen gas (H₂) constitutes 25% of the total moles. If the total pressure inside the container is measured to be 1.24 atm, our objective is to determine the partial pressure of hydrogen gas. This problem illustrates a common situation in chemistry where we need to find the contribution of a specific gas to the overall pressure of a gaseous mixture. Understanding how to solve this type of problem is vital for applications ranging from industrial chemistry to environmental science. The partial pressure of a gas is the pressure that the gas would exert if it occupied the same volume alone. In a mixture of gases, each gas contributes to the total pressure. The contribution of each gas is proportional to its mole fraction in the mixture. This concept is formalized by Dalton's Law of Partial Pressures, which states that the total pressure exerted by a mixture of gases is the sum of the partial pressures of each individual gas. In our case, we are given the total number of moles of gas, the percentage of hydrogen gas, and the total pressure. We need to use these values to calculate the partial pressure of hydrogen. The formula we'll use, Pₑ/Pₜ = nₑ/nₜ, is a direct application of Dalton's Law and the ideal gas law, rearranged to solve for partial pressure. It highlights the relationship between the mole fraction of a gas and its contribution to the total pressure. The ability to perform this calculation is a fundamental skill in chemistry, allowing us to understand and predict the behavior of gaseous systems. So, let's dive into the solution step by step, ensuring a clear understanding of each calculation involved.

To calculate the partial pressure of hydrogen (P(H₂)), we will use the formula:

P(H₂) / Pₜ = n(H₂) / nₜ

Where:

• P(H₂) is the partial pressure of hydrogen
• Pₜ is the total pressure (1.24 atm)
• n(H₂) is the number of moles of hydrogen
• nₜ is the total number of moles (6.4 moles)

Step 1: Calculate the moles of hydrogen gas (n(H₂))

Hydrogen gas makes up 25% of the total moles, so:

n(H₂) = 0.25 * nₜ
n(H₂) = 0.25 * 6.4 moles
n(H₂) = 1.6 moles

This step is crucial because it determines the amount of hydrogen present in the mixture, which directly influences its partial pressure. We start by recognizing that 25% can be expressed as a decimal (0.25). We then multiply this fraction by the total number of moles to find the moles of hydrogen. This calculation stems from the basic principle that a percentage is a proportion of a whole. In this context, 25% represents the proportion of hydrogen moles relative to the total moles of gas. The result, 1.6 moles of hydrogen, is a key value that we will use in the subsequent steps to determine the partial pressure. It's important to understand that the number of moles is a measure of the amount of substance, and it's directly related to the pressure exerted by the gas. The more moles of a gas present in a fixed volume, the higher its partial pressure will be, assuming constant temperature. This relationship is a cornerstone of gas laws and is essential for understanding how gases behave in mixtures. By accurately calculating the moles of hydrogen, we lay the foundation for precisely determining its contribution to the total pressure in the container.

Step 2: Apply the formula to find the partial pressure of hydrogen

Now, we can plug the values into the formula:

P(H₂) / 1.24 atm = 1.6 moles / 6.4 moles

To find P(H₂), we rearrange the equation:

P(H₂) = (1.6 moles / 6.4 moles) * 1.24 atm

P(H₂) = 0.25 * 1.24 atm

P(H₂) = 0.31 atm

This step is where we directly apply the fundamental principle of partial pressures, encapsulated in the formula P(H₂) / Pₜ = n(H₂) / nₜ. By substituting the known values—the total pressure (1.24 atm), the moles of hydrogen (1.6 moles), and the total moles of gas (6.4 moles)—we can isolate the partial pressure of hydrogen. The rearrangement of the equation is a simple algebraic manipulation, multiplying both sides by the total pressure to solve for P(H₂). The ratio of moles of hydrogen to total moles (1.6 moles / 6.4 moles) represents the mole fraction of hydrogen in the mixture. This mole fraction is a dimensionless quantity that indicates the proportion of hydrogen molecules relative to the total number of gas molecules. Multiplying this mole fraction by the total pressure effectively scales the total pressure to reflect the contribution of hydrogen. The calculation yields a partial pressure of 0.31 atm for hydrogen. This means that if hydrogen were the only gas present in the container, it would exert a pressure of 0.31 atm. This value provides a clear understanding of hydrogen's role in the overall pressure within the mixture. The accurate application of this formula and the correct substitution of values are critical for obtaining the correct partial pressure, highlighting the importance of a meticulous approach to problem-solving in chemistry.

The partial pressure of hydrogen gas in the container is 0.31 atm. This result provides a quantitative measure of the contribution of hydrogen to the total pressure within the gaseous mixture. Understanding partial pressures is crucial in many chemical contexts, as it allows us to predict and explain the behavior of gases in various systems. In this specific scenario, knowing the partial pressure of hydrogen helps us understand its role in the overall dynamics of the gas mixture. This information can be further used in more complex calculations, such as determining reaction rates or equilibrium conditions in systems involving gaseous reactants. The ability to calculate partial pressures is not just an academic exercise; it has practical implications in fields like industrial chemistry, environmental science, and even medicine. For instance, in industrial processes, controlling the partial pressures of reactant gases is essential for optimizing reaction yields. In environmental science, understanding the partial pressures of atmospheric gases is crucial for studying phenomena like greenhouse effects and air pollution. In medicine, the partial pressures of oxygen and carbon dioxide in the blood are critical indicators of respiratory function. Therefore, mastering this fundamental concept opens doors to understanding and analyzing a wide range of real-world phenomena. The 0.31 atm partial pressure of hydrogen in this container provides a specific data point that can be integrated into a broader analysis of the system's chemical and physical properties.

In summary, we calculated the partial pressure of hydrogen gas in a container holding a mixture of gases. We began by establishing the problem: a container with 6.4 moles of gas, where hydrogen comprises 25% of the total moles, and the total pressure is 1.24 atm. Our goal was to find the partial pressure of hydrogen. We employed the formula P(H₂) / Pₜ = n(H₂) / nₜ, which directly relates the partial pressure of a gas to its mole fraction within the mixture and the total pressure. The first crucial step involved calculating the number of moles of hydrogen, which we found to be 1.6 moles by multiplying the total moles by the percentage of hydrogen (0.25 * 6.4 moles). This step is fundamental because the amount of hydrogen directly influences its partial pressure contribution. Next, we substituted the known values into the formula. We divided the moles of hydrogen (1.6 moles) by the total moles (6.4 moles) to find the mole fraction of hydrogen, and then multiplied this fraction by the total pressure (1.24 atm). This calculation effectively scales the total pressure to reflect the portion exerted solely by the hydrogen gas. The result of this calculation revealed that the partial pressure of hydrogen is 0.31 atm. This value signifies that if hydrogen were the only gas present, it would exert a pressure of 0.31 atm under the same conditions. This understanding of partial pressures is vital in various contexts, including predicting gas behavior, designing chemical processes, and analyzing gas mixtures in both natural and industrial settings. The ability to accurately calculate partial pressures is a cornerstone skill in chemistry, enabling a deeper comprehension of gas dynamics and their role in chemical systems. The final answer, 0.31 atm, provides a clear and concise quantification of hydrogen's contribution to the total pressure in the given gas mixture.