Question

The molar heat capacity for carbon monoxide at constant volume is cv,m = 20.17 j/(k·mol). a 18.00-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.

Answer 1

The differential change in entropy of a system is given as: 

dS = (∂S/∂T)_V dT 

We also know that

(∂S/∂T)_V = n*Cv/T,

Where Cv is the molar heat capacity at constant volume, and n is the number of moles. Combining the 2 equations:

dS = n*Cv/T dT 

Since Cv is constant as stated in the problem, therefore we integrate the differential equation. Leading us to: 

ΔS = n*Cv*ln(Tfinal/Tinitial) 

We are given that:  V = 18L volume at P=2 kPa and T=298.15K.

Using the ideal gas law to find the number of moles of gas: 

n = p*V/R*T = (2kPa)*(18L)/((298.15K)*(8.314 L*kPa/(mol*K))) 

n = 1.45*10^-2 mol 

Going back to the entropy change: 

ΔS = (1.45*10^-2 mol)*(20.17 J/(K*mol))*ln(1073.15/298.15) 

ΔS = 0.375 J/K