"Diver's" Law

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The name of the discoverer is not known to the ChemTeam. It may even be that this law has never been discovered in the same manner we speak of the discovery of Boyle's Law. Diver is not a name, it refers to diving beneath the water. The deeper you go the greater the pressure because of the larger amount of water pressing down on you.

This law gives the relationship between pressure and amount when the temperature and volume are held constant. Remember, the amount of gas will be measured in moles. Also, since volume is one of the constants, that means the container holding the gas is rigid and cannot change in volume.

If the amount of gas in a container is increased, the pressure increases.

If the amount of gas in a container is decreased, the pressure decreases.

Why?

Suppose the amount is increased. This means there are more gas molecules and this will increase the number of impacts on the container walls. This means the gas pressure inside the container will increase. It will stay at this higher level because the container walls do not move (the volume is constant).

The mathematical form of Diver's Law is:

P  
––– = k
n  

This is a direct mathematical relationship. As one gas variable (either P or n in this law) changes in value, the other variable (P or n) will change in the same direction (either increase or decrease). The constant k will remain the same value.

Let P1 and n1 be a volume-amount pair of data at the start of an experiment. If the amount is changed to a new value called n2, then the pressure will change to P2.

P1  
––– = k
n1  

And we know this:

P2  
––– = k
n2  

Since k = k, we have this:

P1   P2
––– = –––
n1   n2

This equation will be very helpful in solving Diver's Law problems.

Click this sentence for a video using Diver's Law. Instead of moles, the problem uses the word particles. The problem works wih either the word particles or the word moles. That's because, to convert from particles to moles, you divide the number of particles by Avogadro's Number.

What that means is that the ratio of particles is the same value as the ratio of moles.

One example problem in addition to the the video.

Example #1: The relationship between pressure and moles, when volume and temperature of a gas are held constant, is this:

P    
–––  =  k
n    

Which of the following statements is true?

(a) If the number of moles is doubled, the pressure is halved.
(b) If the number of moles if halved, the pressure is doubled.
(c) If the number of moles is tripled, the pressure also triples.
(d) If the number of moles is halved, the pressure is quadrupled.

Solution:

1) Rewrite the relationship:

P = nk

The pressure and number of moles are directly proportional. As either pressure or number of moles changes either up or down in value, the other value changes in the same direction, so as to maintain the equality.

2) Therefore, (c) is the correct answer:

If the number of moles is tripled, the pressure also triples.

3) We don't have to rewrite the relationship to determine that (c) is the correct answer. I just chose to do my answer that way.

4) Here is a demonstration that plugs numbers into the relationship:

Let's assume that, when n = 1, P was measured to also be 1.

That means that k = 1

Now, lets see if (a) is true:

P = nk

0.5 = (2) (1)

We conclude that (a) is not true because 0.5 does not equal 2.


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