Question

A certain volume of a gas had a pressure of 800 torr at a temperature of -40 degrees C. What was the original volume if the volume at STP is now 450.0 cm^3?
(the correct answer is 365 cm^3. I just need an explanation.)

Answer 1

Answer : The original volume of gas is $365cm^3$

Explanation :

Combined gas law is the combination of Boyle's law, Charles's law and Gay-Lussac's law.

The combined gas equation is,

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

where,

$P_1$ = initial pressure of gas = 800 torr

$P_2$ = final pressure of gas at STP = 760 torr

$V_1$ = initial volume of gas = ?

$V_2$ = final volume of gas at STP = $450.0cm^3$

$T_1$ = initial temperature of gas = $-40^oC=273+(-40) =233K$

$T_2$ = final temperature of gas at STP = $0^oC=273+0=273K$

Now put all the given values in the above equation, we get:

$\frac{800torr\times V_1}{233K}=\frac{760torr\times 450.0cm^3}{273K}$

$V_1= 364.8cm^3\approx 365cm^3$

Therefore, the original volume of gas is $365cm^3$