Question

The molar heat capacity for carbon monoxide at constant volume is CV,m = 20.17 J/(K·mol).

A 16.00-L fixed-volume flask contains CO(g) at a pressure of 2.00 kPa and a temperature of 25.0 °C.

Assuming that carbon monoxide acts as an ideal gas and that its heat capacity is constant over the given temperature range, calculate the change in entropy for the gas when it is heated to 800.0 °C.

delta S= _____J/K

Answer 1

Answer

The differential change in entropy of a system for a given differential change in temperature at constant volume is given by:

dS = (∂S/∂T)_V dT

But (∂S/∂T)_V = n*Cv/T, where Cv is the molar heat capacity at constant volume, and n is the number of moles in the system.

dS = n*Cv/T dT

If we assume Cv is constant (as we are directed to in this question), this is easy to integrate, and obtain:

ΔS = n*Cv*ln(T_final/T_initial)

Here, we have a 16L volume at 2*10^3 Pa and 298.15K. Using the ideal gas law to find the number of moles of gas present:

n = p*V/R*T = (2kPa)*(16L)/((298.15K)*(8.314 L*kPa/(mol*K)))

n = 1.29*10^-2 mol

The entropy change is then given by:


ΔS = (1.29*10^-2 mol)*(20.17 J/(K*mol))*ln(1073.15/298.15)

  

      = 0.260 * ln(1073.15/298.15)

           

      = 0.260 * 1.280

ΔS = 0.3328 J/K