Question

A gas sample with a volume of 5.3 L has a pressure of 745 mm Hg at 33°C. What is the pressure of the sample if the volume remains at 5.3 L but the temperature rises to 85°C?

Answer 1

According to the Gay-Lussac which establishes that the pressure of a fixed volume of a gas is directly proportional to its temperature.

It is represented by the following formula:

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

The pressure must be in atm units and temperature in kelvin. We calculate the conversion of each one:

`745\text{ mmHg}\cdot\frac{1\text{ atm}}{760\text{ mmHg}}=0.98\text{ atm,}`
`T_1=33C+273=306K,T_2=85C+273=358K\text{.}`

The final step is clear the final pressure which is P2 and replace the values there:

`P_2=(P_1\cdot T_2)/(T_1)=\frac{0.98\text{ atm}\cdot358\text{ K}}{306\text{ K}}=1.146\text{ atm.}`

Then, we do the conversion from atm to mmHg:

`1.146\text{ atm}\cdot\frac{760\text{ mmHg}}{1\text{ atm}}=870.96\text{ mmHg.}`

The final pressure is 870.96 mmHg.