If 1 10 liter sample of O2 gas at 300 kelvin and 0.5 atmosphere of pressure contains 5.0 x 10^22 molecules how many molecules would a 10 liter sample of H2 have if it was at the same temperature and pressure as the oxygen remember that hydrogens are 1/16th the size of oxygen

Explanation:

The detailed steps and calculations is as shown in the attached file.

 Number of molecules of H2=4.5454375x

Explanation

Given:

P1=P2=0.5 atmosphere=0.505xpa

T1=T2=300k

V1=10 liters of O2

N=5.0x molecules

10 liters of H2

V2=? liters of O2

H2=1/16 of O2

Procedure:

for every liter of H2, there are 16 liters of O2 since H2=1/16 of O2,

Therefore, 10 liters of H2= 160 liters of O2 i.e.

V2=160 liters of O2.

Applying ideal gas equation,

VP=NkT :where P is pressure, V is volume, N is number of molecules, T is temperature in kelvin and k is Boltzman constant=1.38XJ/K.

considering change in volume of O2, N can be calculated as follows:

V1P1=N1kT1..................................(1)

V2P2=N2kT2...............................(2)

dividing (2) by (1)

V2P2/V1P1=N2kT2/N1kT1

but P1=P2 and T1=T2 since they remain the same, they cancel out.

∵ V2/V1=N2/N1

substituting values, we have

160/110=N2/5.0x

N2=1.4545x5.0x =7.2727x molecules of O2

Recall that

N2 of H2=1/16 of N2 of O2

∵Number of molecules of H2=1/16 of 7.2727x

=4.5454x

Number of molecules of H2=4.5454375x