chapter 7 gen chem

Question

A sample of nitrogen gas was collected via water displacement. Because the nitrogen was collected via water displacement, the sample is saturated with water vapor. If the total pressure of the mixture at 21 celsius is 0.983 bar, what is the partial pressure of nitrogen? The vapor pressure of water at 21 celsius is 18.7 mmHg.

Answer 1

TL;DR VERSION:

1. Remember that we can just add up the partial pressures of gases in a mixture to find the total pressure. We have nitrogen gas and water vapor (which is a gas). So our equation looks like this:

Partial pressure of water vapor + partial pressure of nitrogen gas = Total pressure of the mixture

2. We know that the total pressure of the mixture is 0.983 bar (the "bar" is a way to measure gas

pressure). We put this in the equation:

Partial pressure of water vapor + partial pressure of nitrogen gas = 0.983 bar

3 The problem also tells us that the pressure of the water vapor is 18.7 mmHg (the "mmHg" is another way to

measure gas pressure). We put this in the equation like this:

18.7 mmHg + partial pressure of nitrogen gas = 0.983 bar

4 Convert the total pressure (which is currently in "bar") to mmHg with the equation 1 bar = 750.06 mmHg

5 Put the total pressure in mmHg into the equation

6 Do the following to find the partial pressure of nitrogen gas in mmHg:

total pressure in mmHg -- 18.7 mmHg

MORE DETAILED, STEP-BY-STEP VERSION WITH ANSWER BELOW:

The problem gives us a couple important clues. First, the problem says that "the sample is saturated with water vapor". This means that the sample is actually a mixture of water vapor and nitrogen gas. Dalton's Law of Partial Pressures says that we can simply add up the partial pressures of gases in a mixture to find the total pressure. We have two gases (water vapor and nitrogen), so we can write an equation like this:

Partial pressure of water vapor + partial pressure of nitrogen gas = Total pressure of the mixture

The problem says that "the total pressure of the mixture is 0.983 bar". The "bar" is a unit of measurement for gas pressure. In other words, the "bar" is one way to measure the pressure of a gas. Now that we know the total pressure of the mixture = 0.983 bar, we can put the number in the equation like this:

Partial pressure of water vapor + partial pressure of nitrogen gas = 0.983 bar

The problem also says that "the vapor pressure of water is 18.7 mmHg". The "mmHg" is another unit of measurement for gas pressure. In other words, the "mmHg" is another way to measure the pressure of a gas. Now that we know the pressure of water vapor = 18.7 mmHg, we can put the number in the equation like this:

18.7 mmHg + partial pressure of nitrogen gas = 0.983 bar

We can't just subtract, unfortunately. We need to get a single unit of measurement for gas in the equation before we can subtract. In other words, we can't do bar -- mmHg. We can only do bar -- bar or mmHg -- mmHg. Why don't we convert the 0.983 bar into mmHg? That way we won't have to work with tiny numbers like 0.983.

Remember that 1 bar = 750.06 mmHg. We set up our equation like this:

0.983 bar x 750.06 mmHg

1 bar

Now we just multiply straight across, so 0.983 x 750.06 = 737.31. So the total pressure = 737.31 mmHg. We can put this information into the equation like this:

18.7 mmHg + partial pressure of nitrogen gas = 737.31 mmHg

Now we just subtract to find the partial pressure of the nitrogen gas like this:

partial pressure of nitrogen gas = 737.31 mmHg -- 18.7 mmHg

The calculator says that 737.31 -- 18.7 = 718.61. So the partial pressure of the nitrogen gas = 718.61 mmHg.

If you need the partial pressure of the nitrogen gas in bar instead of mmHg, we set up this equation:

718.61 mmHg x 1 bar

750.06 mmHg

We solve this equation by doing 718.61/750.06. The calculator says that 718.61/750.06 = 0.958. So we can also express the pressure of the nitrogen gas as 0.958 bar.

Final Answer: The pressure of the nitrogen gas is 718.61 mmHg (or, if the partial pressure needs to be in bar, 0.958 bar)