### 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.