Dalton's Law of Partial Pressures: HW problems

1. Consider Dalton’s Law of Partial Pressures:
Ina. Restate the law (put it into your own words) Answer
Inb. Consider a closed container with 7 atm of gas inside. There are 2 mol of gas X, 5 mol of gas Y, and 7 mol of gas Z. The gasses do not interact with each other, and thus Dalton’s Law of Partial Pressures applies. What are the partial pressures of each of the three gases? Answer
Inc. Consider another closed container. Inside, there are 2 mol gas A. When we add 3 mol of gas B, we see that the total pressure inside the cylinder increases by 6 atm. If gas A does not interact with gas B, what was the original pressure in the cylinder? Hint: Hint 2 Hint 3 Answer


HINTS:
1.c.
Hint 1: Another way of looking at Dalton’s Law of Partial Pressures tells us that as long as the gases in a container don’t interact, their pressures are independent. In other words, as long as the pressures don’t interact, we can apply PV=nRT to them independently.

Hint 2: Since the pressures of A and B are independent, the partial pressure of gas A doesn’t change when we add gas B.

Hint 3: Since the partial pressure of gas A doesn’t change when we add gas B, we can calculate A’s partial pressure after we add gas B, as the pressure will be the same.


ANSWERS:
Question 1
Part a
Dalton tells us that, if we have more than one gas in an enclosed container, and those gases don't react, then the ratio of each gas's partial pressure to the total of the pressure of all of the gases equals the ratio of the moles of each gas present to the total number of moles of gas present.

Part b
gas X: 1 atm; gas Y: 2.5 atm; gas Z: 3.5 atm
Explanation: Initially, we have:

2 mol gas X	= ? atm
+ 5 mol gas Y	= ? atm
+ 7 mol gas Z	= ? atm
= ? mol	= 7 atm

We can easily fill in the total number of moles:

2 mol gas X	= ? atm
+ 5 mol gas Y	= ? atm
+ 7 mol gas Z	= ? atm
= 14 mol	= 7 atm

Now, we can determine the ratio of moles to atmospheres: 14 moles to 7 atm, which reduces to 2 mol to 1 atm, or 1 mol to 0.5 atm. We then apply this ratio to the individual gases:

2 mol gas X	= 1 atm
+ 5 mol gas Y	= 2.5 atm
+ 7 mol gas Z	= 3.5 atm
= 14 mol	= 7 atm

Note that the pressure each gas individually adds up to the total pressure in the container.


Part c
4 atm
Explanation: Dalton tells us that, if gasses don't interact with each other, for a given volume and temperature the ratio of moles to presure is fixed. When we added three moles of gas B, we saw that it generated 6 atm, telling us that the ratio of moles:atm was 3:6, or 1:2. Since there are two moles of gas A, these moles exert 4 atm.


Last edited July 26, 2008