# Considering the ideal gas law PV = nRT, what is P directly proportional to?

##### 1 Answer

Here's what's going on here.

#### Explanation:

First, make sure that you have a clear understanding of what *directly proportional* actually means.

In order for two quantities to be directly proportional, you need one to **increase** as the other increases or **decrease** as the other decreases, in both cases **at the same rate**.

Starting from the ideal gas law equation, isolate

#PV = nRT implies P = (nRT)/V#

Since **constant**, you can write it separately

#P = (nT)/V * R#

Now focus on the ratio that exists between *number of moles*, *temperature*, *volume*,

Let's start with the number of moles. In order to establish direct or inverse proportionality, you need to **keep the other two variables** constant.

#P = n * overbrace(T/V * R)^(color(blue)("constant"))#

So, under these circumstance, what would happen to **increase**? Well, in order for the equal sign to remain valid, **Increase** as well.

Likewise, if **decrease**, **decrease** as well. Therefore, you can say that

Pressure is directly proportional with number of moleswhentemperature and volume arekept constant

The same can be said for temperature,

#P = T * overbrace(n/V * R)^(color(blue)("constant"))#

Once again, an **increase** in temperature will result in an **Increase** in pressure, and a **decrease** in temperature will result in a ** decrease** in pressure. Therefore, you can say that

Pressure is directly proportional with temperaturewhennumber of moles and volume arekept constant- Gay Lussac's Law

Finally, keep number of moles and temperature constant and check to see what happens to pressure when the volume varies.

#P = 1/V * overbrace(n * T * R)^(color(blue)("constant"))#

This time, an **increase** in volume would result in a **decrease** in pressure, since volume is now in the *denominator*

#V uarr implies 1/V darr#

Likewise, a **decrease** in volume would result in an **increase** in pressure. Therefore, pressure **is not** directly proportional to volume when number of moles and temperature are kept constant.

You can say, however, that

Pressure is inversely proportional with volumewhennumber of moles and temperature arekept constant- Boyle's Law