Video: Identifying the Expression for the New Volume of Hydrogen Gas That Was Produced in an Experiment Where Zinc and Hydrochloric Acid Were Reacted Together, Given the Initial and Final Conditions

An experiment is performed to determine the amount of hydrogen gas released in a reaction. Hydrogen gas is released by reacting hydrochloric acid with zinc metal according to the given equation. Zn(s) + 2HCl(aq) ⟶ ZnCl₂(aq) + H₂(g) All of the Zn metal was consumed, and hydrogen gas was collected by displacement of water in an inverted bottle. The following data is obtained. What would the volume of hydrogen gas be at 1 atm and 25°C? [A]((50.8)(751.2 − 23.8))/760 mL [B] ((50.8)(751.2 + 23.8))/760 mL [C] ((50.8)(751.2 − 23.8))/751.2 mL [D] (751.2 − 23.8)/(760)(50.8) mL [E] (760 − 23.8)/(751.2)(50.8) mL

06:25

Video Transcript

An experiment is performed to determine the amount of hydrogen gas released in a reaction. Hydrogen gas is released by reacting hydrochloric acid with zinc metal according to the given equation. Zn solid plus 2HCl aqueous react to form ZnCl₂ aqueous plus H₂ gas. All of the Zn metal was consumed, and hydrogen gas was collected by displacement of water in an inverted bottle. The following data is obtained. What would the volume of hydrogen gas be at one atmosphere and 25 degrees Celsius? Our answer choices are different mathematical expressions with numbers taken from the table given in the problem.

In the experiment that’s described in this question, we’re reacting zinc metal with hydrochloric acid with the goal of determining the amount of hydrogen gas that’s released as a result of the reaction. So we’re using this experimental setup to help us accomplish that goal. As the hydrogen gas is produced in this reaction, it will travel to the inverted bottle, which is initially filled with water. As the hydrogen gas is produced, it will displace some of the water that’s in the bottle. And we can use that to figure out how much hydrogen gas is collected during the course of the experiment.

There’s one thing that complicates this experiment, though, and that’s the fact that, at any given temperature, there’s always going to be some amount of water that is able to evaporate. And since we’re collecting our hydrogen gas over water, that means it’s not just hydrogen gas that’s going to be in the inverted bottle. We’ll also have some water vapour present as well. To account for this, the first thing that we need to do is make sure the water level inside the bottle is the same as outside the bottle. This will make sure that the pressure from the atmosphere pushing down outside the bottle is the same as the pressure from the hydrogen gas and the water vapour inside the bottle.

In other words, if the water levels are equal, the atmospheric pressure will be equal to the pressure of the hydrogen gas plus the pressure of the water vapour. The atmospheric pressure is an easy quantity to measure. And the vapour pressure of water is something that we can look up in a table as long as we know the temperature of the room, since the amount of water that will evaporate will change depending on the temperature. This allows us to easily solve for the pressure of the hydrogen gas that we’ve collected, which allows us to accomplish our goal of determining the amount of hydrogen gas that was released as a result of the reaction.

In this question, we’re being asked to determine the volume of the hydrogen gas that we collected would be at one atmosphere and 25 degrees Celsius. In this experiment, the pressure was measured in units of millimetres of mercury. One atmosphere is equal to 760 millimetres of mercury. So one atmosphere is higher than the pressure that we perform this experiment at. Before we go any further, let’s take a look at the numbers that are used in the answer choices so we can figure out what’s going on.

This 50.8 is the volume of the gas that was collected over water. So this would be the volume of our hydrogen gas. 751.2 was the atmospheric pressure when the experiment was conducted. 23.8 is the vapour pressure of water at 25 degrees Celsius. And 760 is the pressure of one atmosphere given in units of millimetres of mercury, which is what this question is asking about.

To solve this problem, we’re going to use Boyle’s law, which tell us that pressure and volume are inversely proportional if the temperature is held constant. 𝑃 one and 𝑉 one will be the pressure and volume of the hydrogen gas under the conditions that the experiment was conducted. 𝑃 two and 𝑉 two will be the pressure and volume of the hydrogen gas under the new conditions, that is, the conditions given in the question, one atmosphere and 25 degrees Celsius. This 𝑉 two is what the question is asking about. So let’s see if we can rearrange Boyle’s law to create an expression for 𝑉 two.

We can easily accomplish this by dividing both sides of the equation by 𝑃 two, which will give us 𝑉 two is equal to 𝑃 one times 𝑉 one divided by 𝑃 two. So now, let’s go through each of these variables to figure out what they’d be. 𝑃 two is easy. That would be the pressure that the question is asking for, one atmosphere, which would be equal to 760 millimetres of mercury. 𝑉 one is the volume of the hydrogen gas that was collected under the conditions of the experiment. This would be the volume of the gas collected over water in our table. 𝑃 one is the pressure of the hydrogen gas that was collected during the experiment. This number is not given on the table, but I’ve written an equation already that contains this value.

We can easily solve for the pressure of the hydrogen gas that was collected by subtracting the vapour pressure of water at 25 degrees Celsius from the atmospheric pressure. So now, we have numerical values for all of the variables in our equation to solve for the volume of hydrogen gas at one atmosphere and 25 degrees Celsius. If we plug in numbers for all of the variables, the result that we get matches answer choice A. According to Boyle’s law, pressure and volume are inversely proportional. And since the pressure that this question is asking about was higher than the atmospheric pressure that was measured when the experiment was conducted, the volume of the hydrogen gas should decrease. But answer choice A is the correct expression to represent the volume of the hydrogen gas at one atmosphere and 25 degrees Celsius.

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