Question

A gas occupies 50 L at a pressure of 2 atm. What is the volume when the pressure is increased to 10 atm?

Answer 1

`10` `"L"`

Explanation:

We're asked to calculate the new volume of a gas when its pressure is increased.

To solve this, we can use the pressure-volume relationship of gases, illustrated by Boyle's law:

`P_1V_1 = P_2V_2`

where

• `P` is the initial (`"1"`) and final (`"2"`) pressure of the gas, and

• `V` is the initial (`"1"`) and final (`"2"`) volume of the gas.

Let's plug in our known variables, and rearrange this equation to solve for the final volume, `V_2`:

`V_2 = (P_1V_1)/(P_2) = ((2cancel("atm"))(50"L"))/(10cancel("atm")) = color(red)(10"L"`

Thus, when the pressure of the gas was increased by a factor of `5` (`2"atm"` to `10"atm"`), the volume decreased by a factor of `5` (`50"L"` to `10"L"`).