A-level chem enthalpy question

Hey guys, came across this question and can’t figure it out. Would really appreciate it if someone could talk me through a solution!
Here it is:

Estimate the mean bond enthalpies of the P-Cl bond in PCl3(l).

Enthalpy change of formation: PCl3 (l) = -320
Enthalpy changes of atomisation: phosphorus = +315, chlorine = +122
Enthalpy change of vaporisation: PCl3(l) = +33

I know I have to draw a Hess’ cycle but can’t figure out how to connect all the different state changes and put in the right values.

I’d first try to understand what the enthalpy changes represent:

Bond enthalpies represent the enthalpy change when 1.00 mol of a bond is broken in the gas phase: as such, you should be considering PCl3 (g) in your calculations, but data is given for the formation of PCl3 (l).

Atomisation enthalpies show the enthalpy changes when elements in their standard states are converted to 1.00 mol of gaseous atoms.

As such, P (s) —> P (g) and 1/2Cl2 (g) —> Cl (g) would be the equations for the given enthalpies of atomisation.

You can use the enthalpies of formation and vaporisation for PCl3 (l) to work out the enthalpy of formation of PCl3 (g).

So three processes should be considered:

-The conversion of P (s) and an appropriate quantity of Cl2 (g) to P (g) and an appropriate quantity of Cl (g), respectively.

-The formation of PCl3 (g) directly from the elements in their standard states.

-The breakdown of all three P-Cl bond in PCl3 (g) to produce gaseous atoms.


Let us call the bond enthalpy of P-Cl ‘x’ kJ mol^-1.

Can you now calculate the enthalpy changes for the first two processes and write an expression for the enthalpy change of the third process in terms of x?

Can you now draw a Hess cycle and fill in the arrows as appropriate?

Hi, thanks so much for helping out. I’ve figured it out now, it was the state changes between liquids and gases that was throwing me off.

I drew out the cycle like you said and got the calculation:

-320 + 33 + 3(P-Cl) = 3 x 122 + 315
-287 + 3(P-Cl) = 681
3(P-Cl) = 968/3

P-Cl = 322.6 kJmol-1

I checked with the mark scheme and this is the right answer!