Physical Chemistry 2. By definition, the compression factor of an ideal gas is Z

Question

Physical Chemistry

2. By definition, the compression factor of an ideal gas is Z - 1. a. What would be the value of Z for nitrogen at 300 Kand 1 atm, f we calculate 2 using the virial equation (including only the coefficient B, the second virial coefficient)? For nitrogen, B =-3.91 cm3/mol. Repeat the calculation for water vapor. For water vapor, B =-1126 cm3/ mol. Use the ideal gas equation to determine the molar volume at 300k and 1 atm. b. Compare the results for both gases and explain the physical reasons for their difference.

Explanation / Answer

Solution:-

For nitrogen, temperature = 300K pressure = 1 atm

Z = 1+ B(T)1/Vm

B = virial coefficient for nitrogen B = -3.91 cm3/mol (given)

Vm = molar volume , molar volume can be calculated using ideal gas equation PVm = nRT P = pressure = 1 atm T = temperature = 300k R = gas constant = 0.08205 L atm / (mol) K n = 1 mol ( we are calculating molar volume )

so Vm = nRT/P = (1 mol * (0.08205 L atm / (mol) K )*300K )/1atm = 24.615 L = 24615 cm3/mol [ 1L = 1000 cm3]

Now we can calculate Z, Z = 1+ B(T)1/Vm = 1+ (-3.91 cm3/mol)/24614 cm3/mol = 0.9998 Z for nitrogen is 0.09998

similarly we will calculate for oxygen

Vm = 24615 ( calculated above , all the conditions are same )

Z = 1+ B(T)1/Vm = 1+ (-1126 cm3/mol)/24614 cm3/mol = 0.9542 Z for water is 0.9542

z for oxygen is less the z for nitrogen

b) from the above compression fector for water is less then for nitrogen , z for nitrogen nore closer to 1 as compared to water so we can say that nitrogen behaves more like ideal gas then water and a very important reason lies behind the structure of both the gases.

water has three atom and it shows very good hydrogen bonding between the moleule whereas two nitrogen atoms are bonded via triple bond and become very inert so in nitrogen two nitrogen molecule has no interaction. For ideal gases we assume no molecular interaction as here water shows strong hydrogen bonding between the molecule but nitrogen does not show any interaction so nitrogen is more like ideal gas not water.

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