When 229 J of energy is supplied as heat at constant pressure to 3 mol Ar(g), the temperature of the sample is increased by 2.55K. Calcate molar heat capacity at constant volume?

Question

Answer

Answer

Calculation of Molar Heat Capacity at Constant Volume of Argon Gas

In order to calculate the molar heat capacity at constant volume of argon gas, we need to use the following formula:

Cv = (ΔU / nΔT)

Given Data

Energy supplied as heat (q) = 229 J

Number of moles of argon gas (n) = 3 mol

Change in temperature (ΔT) = 2.55 K

Calculations

Since the pressure is constant, the energy supplied as heat (q) is equal to the change in enthalpy (ΔH).

Therefore, we can use the following formula:

ΔH = q = nCpΔT

where Cp is the molar heat capacity at constant pressure.

Substituting the given values, we get:

Cp = ΔH / nΔT = 229 J / (3 mol x 2.55 K) = 29.0 J/(mol K)

Next, we can use the relationship between Cp and Cv to calculate the molar heat capacity at constant volume (Cv).

Cp - Cv = R

where R is the gas constant.

For argon gas, R = 8.31 J/(mol K).

Therefore, we can calculate Cv as:

Cv = Cp - R = 29.0 J/(mol K) - 8.31 J/(mol K) = 20.7 J/(mol K)

Conclusion

The molar heat capacity at constant volume of argon gas is 20.7 J/(mol K).

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