Hydrogen Gas Over Water: A Chemistry Calculation

Have you ever wondered what happens when a chemist collects hydrogen gas over water? It's a common laboratory technique, and it leads to a fascinating outcome: you end up with a mixture of hydrogen gas and water vapor in your collecting bottle. This scenario presents a classic chemistry problem, especially when you need to figure out the partial pressure of the hydrogen gas itself. Let's dive into how we can solve this, using the information provided. When a chemist collects hydrogen gas over water, the total pressure inside the collection vessel isn't just from the hydrogen; it's also influenced by the water molecules that have evaporated into the gas phase. This is a direct application of Dalton's Law of Partial Pressures, a fundamental concept in chemistry that states the total pressure of a gas mixture is equal to the sum of the partial pressures of each individual gas in the mixture. In our case, the collecting bottle contains both hydrogen gas ($H_2$) and water vapor ($H_2O$). Therefore, the total pressure we measure is the sum of the partial pressure of hydrogen and the partial pressure of water vapor. The challenge, then, is to isolate the pressure exerted solely by the hydrogen gas. We are given the total pressure inside the collecting bottle, which is 97.1 kilopascals (kPa). We are also given the vapor pressure of the water at the prevailing temperature, which is 3.2 kilopascals (kPa). The vapor pressure of water is essentially the pressure exerted by the water molecules that have escaped from the liquid surface into the gaseous state. This vapor pressure is dependent on temperature; higher temperatures mean more evaporation and thus a higher vapor pressure. In this specific problem, we are provided with this value, simplifying our calculation. So, how do we find the partial pressure of hydrogen? It's quite straightforward when you understand Dalton's Law. The equation we use is: $P_{total} = P_{H_2} + P_{H_2O}$, where $P_{total}$ is the total pressure, $P_{H_2}$ is the partial pressure of hydrogen gas, and $P_{H_2O}$ is the partial pressure of water vapor. To find the partial pressure of hydrogen ($P_{H_2}$), we simply rearrange the formula to: $P_{H_2} = P_{total} - P_{H_2O}$. This means we subtract the pressure contributed by the water vapor from the total measured pressure. This is the key step in isolating the pressure of the gas we are interested in, which is hydrogen in this scenario. It’s a practical demonstration of how gases behave in a mixture and how we can quantify their individual contributions to the overall pressure. This principle is vital in many areas of chemistry, from understanding atmospheric pressure to designing chemical reactions. The ease of this calculation hinges on having accurate measurements for both the total pressure and the vapor pressure of the liquid. In a real lab setting, ensuring the temperature is stable is crucial for obtaining an accurate vapor pressure value. Without this information, calculating the partial pressure of the collected gas would be significantly more complex. This foundational knowledge helps us appreciate the subtle interactions happening within a seemingly simple collection of gases.

The Calculation: Applying Dalton's Law

Now, let's get down to the actual calculation. We have the total pressure in the collecting bottle, which is 97.1 kilopascals (kPa). We also know the vapor pressure of the water, which is 3.2 kilopascals (kPa). As established by Dalton's Law of Partial Pressures, the total pressure is the sum of the partial pressures of all the gases present. In this collection bottle, we have hydrogen gas and water vapor. So, the equation is: $P_{total} = P_{H_2} + P_{H_2O}$. Our goal is to find the partial pressure of the hydrogen gas ($P_{H_2}$). To do this, we rearrange the equation: $P_{H_2} = P_{total} - P_{H_2O}$. Now, we substitute the given values into the rearranged equation: $P_{H_2} = 97.1 ext{ kPa} - 3.2 ext{ kPa}$. Performing the subtraction, we get: $P_{H_2} = 93.9 ext{ kPa}$. Therefore, the partial pressure of the hydrogen gas collected over water is 93.9 kilopascals. This value represents the pressure that the hydrogen gas molecules alone are exerting on the walls of the collecting bottle. It’s important to note that this calculation assumes the hydrogen gas itself does not significantly react with or dissolve in the water. In most standard laboratory conditions for collecting hydrogen over water, these assumptions are generally valid. The simplicity of this calculation underscores the elegance of Dalton's Law. It allows us to dissect complex gas mixtures into their individual components, provided we have the necessary data. This method is not just theoretical; it's a practical tool used by chemists to understand reaction yields, gas compositions, and the physical behavior of gases under various conditions. For instance, if a chemist were trying to determine the exact amount of hydrogen produced in a reaction, knowing its partial pressure is a crucial first step. This information can then be used with the ideal gas law ($PV=nRT$) to calculate the number of moles of hydrogen gas collected. The temperature would be essential here, as it affects the vapor pressure of water and is a direct variable in the ideal gas law. The technique of collecting gases over water is particularly useful for gases that are insoluble or only slightly soluble in water, like hydrogen, oxygen, and nitrogen. For gases that readily dissolve in water, like ammonia or hydrogen chloride, this method would not be suitable, and alternative collection methods would be required. Understanding partial pressures helps chemists predict and control experimental outcomes, making it a cornerstone of quantitative chemistry. It highlights how each gas in a mixture behaves independently regarding pressure, irrespective of the presence of other gases, as long as they don't interact chemically.

Why is This Important in Chemistry?

Understanding how to calculate the partial pressure of hydrogen gas collected over water is more than just an academic exercise; it's a practical skill with real-world implications in various chemical contexts. When chemists collect gases using the displacement of water method, they are essentially working with a mixture. Knowing the partial pressure of the desired gas, in this case, hydrogen, is crucial for several reasons. Firstly, it allows for accurate determination of the amount of gas collected. Using the ideal gas law ($PV=nRT$), where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature, chemists can calculate the number of moles (n) of hydrogen gas. To do this accurately, you must use the partial pressure of hydrogen, not the total pressure, as the 'P' in the equation. If you used the total pressure, your calculated number of moles would be incorrect, leading to errors in yield calculations or stoichiometric analyses. Secondly, this knowledge is vital for understanding gas stoichiometry. Many chemical reactions involve gases, and predicting the volume or amount of gas produced or consumed relies on accurate pressure measurements. For reactions where a gas is collected over water, accounting for the water vapor’s contribution to the total pressure ensures that calculations related to the reaction's progress are precise. Imagine a synthesis reaction where you expect to produce a certain volume of hydrogen gas. If you collect it over water and don't correct for vapor pressure, you might underestimate the actual volume of hydrogen produced, leading to a mistaken conclusion about the reaction's efficiency. Thirdly, it helps in understanding the physical properties of gases and their behavior in mixtures. Dalton's Law of Partial Pressures is a fundamental principle that governs the behavior of gases. By applying it, we reinforce our understanding that each gas in a mixture contributes to the total pressure independently of the others. This principle is also essential when studying gas diffusion, gas solubility, and atmospheric science. The partial pressure of water vapor, for instance, is a key factor in determining humidity levels. In a broader sense, this calculation is a building block for more complex gas law applications. It prepares students and researchers for scenarios involving gas mixtures in various industrial processes, environmental monitoring, and analytical chemistry techniques. The method of collecting gases over water is a historical and still relevant technique, especially for gases that don't readily dissolve in water. Its continued use highlights the practical importance of understanding and calculating partial pressures in a laboratory setting. It’s a fundamental concept that bridges theoretical knowledge with hands-on experimental work, making chemistry tangible and understandable. This detailed understanding ensures that experimental data is interpreted correctly, leading to sound scientific conclusions and advancements.

For further reading on gas laws and their applications, you can explore resources from The American Chemical Society.