Question

A sample of argon has a volume of 0.43 ml at 24 C. At what temperature in degrees Celsius will it have a volume of 0.57mL?

Answer 1

The sample of argon will have a volume of `"0.57 mL"` at `24^@"C"`.

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 if the temperature increases, the temperature increases, and vice versa. The formula for this gas law 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 first be converted to Kelvins. At the end, the Kelvin temperature can be converted to degrees Celsius.

Known

`V_1="0.43 mL"`

`T_1="24"^@"C + 273.15"="297 K"`

`V_2="0.57 mL"`

Unknown

`T_2`

Solution

Rearrange the formula to isolate `T_2`. Plug in the known values and solve.

`T_2=(V_2T_1)/V_1`

`T_2=(0.57color(red)cancel(color(black)("mL"))xx297"K")/(0.43color(red)cancel(color(black)("mL")))="390 K"` (rounded to two significant figures)

`"297 K"-"273.15"="24"^@"C"`