Question

Using the same sample of gas (P1 = 775 torr, Ti = 39 °C), we wish to change the pressure to 7750 torr with no

accompanying change in volume or amount of gas. What temperature T2, in Celsius, is needed to reach this
pressure?
Express your answer with the appropriate units.

Answer 1

Answer: The temperature that is needed to reach this pressure is
`2847^oC`.

Step-by-step explanation:

To calculate the temperature with changing pressure, we use the equation given by Gay Lussac law.

This law states that pressure is directly proportional to the temperature of the gas at constant volume and the number of moles.

Mathematically,

`P\propto T` (At constant volume and number of moles)

The equation given by this law is:

`(P_1)/(T_1)=(P_2)/(T_2)`

where,

`P_1\text{ and }T_1` are initial pressure and temperature

`P_2\text{ and }T_2` are final pressure and temperature

Given values:

`P_1=775 torr\\T_1=39^oC=[39+273]K=312K\\P_2=7750 torr\\T_2=?`

Plugging values in the above equation:

`(775 torr)/(312K)=(7750 torr)/(T_2)\\\\T_2=(7750* 312)/(775)\\\\T_2=3120K`

Converting it into degree Celsius:

`T(^oC)=3120-273=2847^oC`

Hence, the temperature that is needed to reach this pressure is
`2847^oC`.