We assume the gas obey the ideal gas laws, or in other words the general equation of gases is respected:
`P*V =N*R*T` (1)
where `N` is the number of gas moles and `R =8.13 J/(K*mol)` is the universal gas constant.
The standard conditions of temperature and pressure (STP) are defined by IUPAC as being `t = 0 @C (273.15 K)` and `P =10^5 N/m^2` .
From the above equation (1) one can deduce that for the same quantity of gas (same number of moles `N` ) the relation between the initial and final states is:
With the data in the text one has
`P_1 =752 "torr" =752*133.322 Pa =100258 N/m^2`
`V_1 =53.5 mL`
`T_1 =15+273.15 =288.15 K`
`P_2 =10^5 N/m^2`
`T_2 =273.15 K`
`V_2 =V_1*(P_1/P_2)*(T_2/T_1) =53.5*100258/100000*273.15/288.15 =50.84 mL`
Answer: the volume of the sample of gas at STP conditions is 50.84 mL