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

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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`


`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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