[confusedcollegestudent]

The enthalpy of vaporization of carbon tetrachloride (CCl₄) is 30.5 kJ∙mol^–1 at its normal boiling temperature of 350 K. Given that the constant pressure molar heat capacities of liquid and gaseous CCl₄ are 83.5 and 135.0 J∙K^–1∙mol^–1, respectively, the enthalpy of vaporization of CCl₄ at 545 K is ______________kJ∙mol⁻¹.

How would I begin with problem?
I've tried to use ΔS_vap = Δ_vapH / T_b and that didn't give me the proper answer.
The right answer is 40.5 kJ/mol and I'm really stuck on how to begin this problem.

[Enthalpy]

Find a sequence of operations that includes the evaporation at 545K and is equivalent to the evaporation at 350K.

Except that the question is rotten, mouldy and wormy, because the critical temperature is 556K
https://en.wikipedia.org/wiki/Carbon_tetrachloride_(data_page)
so the heat capacities are definitely not constant up to 545K.

The liquid's heat capacity exceeds the gas' one. It's 135 and 83 J/mol/K, not the opposite. Quite common among substances, I know no exception up to now.
Consequently, the heat of vaporization decreases with a warmer temperature, especially if nearing the critical temperature where it converges to zero. Certainly not 40.5 kJ/mol hence.

Who is the bozo who gave you this question?