Question

A gas at standard temperature (0°C) has a volume of 30.50 Liters and a pressure of 931 torr.What is the volume at standard pressure ?

Answer 1

The final volume will be `"37.9 L"`.

Explanation:

Standard temperature for gas laws is `"273.15 K"`, and standard pressure is `"100 kPa"`.

Since the temperature remains constant, we can drop it as a variable. We would then have two variables, volume and pressure. Boyle's law describes the relationship between volume and pressure of a gas, which states that the pressure and volume of a gas are inversely proportional. This means that if the pressure increases, the volume decreases, and vice versa. The formula for Boyle's law is:

`P_1V_1=P_2V_2`

Known

`P_1=931color(red)cancel(color(black)("torr"))xx("1 kPa")/(7.500638color(red)cancel(color(black)("torr")))="124.12 kPa"`
`V_1="30.50 L"`

`P_2="100 kPa"`

Unknown

`V_2`

Solution

Rearrange the equation to isolate `V_2`, plug in the known values and solve.

`V_2=(P_1V_1)/(P_2)`

`V_2=(124.12color(red)cancel(color(black)("kPa"))xx30.50"L")/(100color(red)cancel(color(black)("kPa")))="37.9 L"` (rounded to three significant figures)