Question

A sample of gas at `"31"^@"C"` has a pressure of `"745 Torr"`. What is the pressure if the temperature is increased to `"78"^@"C"`?

Answer 1

The final pressure will be `"860. torr"`.

Explanation:

This is an example of Gay-Lussac's law , which states that the pressure of a gas with a constant volume and amount, is directly proportional to the temperature in Kelvins. This means that if the pressure is increased, the temperature will increase, and vice-versa.

The equation that is used for this law is:

`P_1/T_1=P_2/T_2`

where `P_1` is the initial pressure, `P_2` is the final pressure, `T_1` is the initial temperature, `T_2` is the final temperature.

Write what is known.
`P_1="745 torr"`
`T_1="31"^@"C" + 273.15=304 "K"`
`T_2="78"^@"C" + 273.15=351 "K"`

Write what is unknown: `P_2`

Solution
Rearrange the equation to isolate `P_2`. Substitute the known values into the equation and solve.

`P_2=(P_1T_2)/T_1`

`P_2=(745"torr"xx351color(red)cancel(color(black)("K")))/(304color(red)cancel(color(black)("K")))="860. torr"` (rounded to three significant figures)

Answer 2

`P_2 = 860` torr

Explanation:

With a constant container volume, Charles' Law becomes simply:
`P_1/T_1 = P_2/T_2`
Rearrange for your known values:

`P_2 = P_1 * T_2/T_1` ; `P_2 = 745 * 351/304` ; `P_2 = 860` torr

The ideal gas law (Charles' Law) states:
`(P_1 * V_1)/T_1 = (P_2 * V_2)/T_2`
Where `P_1,_2` are pressures – units don't matter in this case as long as they are consistent, because this is a ratio.
`V_1,_2` are the corresponding volumes in Liters
`T_1,_2` are the temperatures in degrees Kelvin