At what temperature a gas with volume 175 L at 15 oC and 760mmHg will occupy a volume of 198 L at a pressure 640mmHg?

To calculate the pressure when temperature and volume has changed, we use the equation given by combined gas law. The equation follows:

\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}

T

1

P

1

V

1

=

T

2

P

2

V

2

where,

P_1,V_1\text{ and }T_1P

1

,V

1

and T

1

are the initial pressure, volume and temperature of the gas

P_2,V_2\text{ and }T_2P

2

,V

2

and T

2

are the final pressure, volume and temperature of the gas

We are given:

\begin{gathered}P_1=760mmHg\\V_1=175L\\T_1=15^oC=[15+273]K=288K\\P_2=640mmHg\\V_2=198L\\T_2=?K\end{gathered}

P

1

=760mmHg

V

1

=175L

T

1

=15

o

C=[15+273]K=288K

P

2

=640mmHg

V

2

=198L

T

2

=?K

Putting values in above equation, we get:

\begin{gathered}\frac{760mmHg\times 175L}{288K}=\frac{640mmHg\times 198L}{T_2}T_2=274K\end{gathered}

288K

760mmHg×175L

=

T

2

640mmHg×198L

T

2

=274K

Hence, the temperature when the volume and pressure has changed is 274 K

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