# A hydrogen sample gas collected over water at 15°C and 752 torr occupies 53.5 mL. Calculate its volume at STP conditions. 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:

`(P_1*V_1)/T_1 =(P_2*V_2)/T_2`

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`

Thus

`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

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