Question

A 10.00L vessel containing CO2 has an internal pressure 20.0 atm, at 0°C. Calculate the number of moles of gas using: (Hint: The method might be 8th grade algebra but some computer or graphing power may be needed. a. the virial equation (B=-149.7 at 273 K)b. van der Waals equation (a=3.610 b=4.29) c. To within an uncertainty of 0.5 % does it matter which equation you use to find it? Why? d. Would it matter if the same sample was measured 100 atm and 600K?

Answer 1

Given data

V = 10 L

Temp (T) = 0 + 273 = 273 K

P = 20 atm

R = gas constant = 8.314

For moles of gas we need to apply the ideal gas equation.

PV = nRT , n = moles of gas, in this case CO2

Virial equation : pV/nRT = Z = 1+ B(T)n/V

and van der waals equation: [P + a(n/V)^2] (V/n - b) = RT

solving these two equation also gives us values similar to ideal gas equation

putting the data in equation

20 * 10 = n * 8.314 * 273

n = 200/273*8.314 = 0.088 moles

now if conditions are 100atm and 600K temperature,

put the values in equation

100*10 = n * 8.314* 600

moles (n) = 1000/600*8.314 = 0.2 moles

Answer, Hope this helps you