Question

The volume of a gas is 5.0 L when the temperature is 5.0 C. If the temperature is increased to 10.0 C without changing the pressure what is the new volume?

Answer 1

The new volume will be `"5.1 L"`.

Explanation:

This is an example of Charles' law , which states that the volume of a given amount of gas held at constant pressure is directly proportional to the Kelvin temperature. This means that as the volume increases, so does the temperature, and vice versa. The equation is:

`V_1/T_1=V_2/T_2`,

where:

`V_1` and `T_1` are the initial volume and temperature, and `V_2` and `T_2` are the final volume and temperature.

The temperature must be in Kelvins, so you need to add `"273.15"` to the Celsius temperatures.

Known

`V_1="5.0 L"`

`T_1="5.0"^@"C + 273.15"="278.2 K"`

`T_2="10.0"^@"C + 273.15"="283.2 K"`

Unknown

`V_2`

Solution

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

`V_2=(V_1T_2)/T_1`

`V_2=(5.0"L"xx283.2"K")/(278.2"K")="5.1 L"` (rounded to two significant figures)

The new volume will be `"5.1 L"`.