How do I calculate the temperature change in a gaseous reaction?

So, with $\pu{3 mol}$ of $\ce{H2}$ and $\pu{3 mol}$ of $\ce{Cl2}$ and given the reaction $\ce{H2(g) + Cl2(g) -> 2 HCl(g)}$ with $\Delta H=\pu{-184.6 kJ/mol}$, I am supposed to calculate the work done on the surroundings of the system at $\pu{1 atm}$ and $\pu{25^\circ C}$.


My current thought process for this is to calculate the enthalpy change of the system first, which is $\Delta H \cdot n\_{\ce{H2}}=\pu{-553.8 kJ}=-q\_{\mathrm{rxn}}$. Assuming constant pressure, I tried to calculate $\Delta T=\frac{q}{m\cdot c}$, so I could calculate the volume change through the Ideal Gas law and then calculate the work $w=P\cdot \Delta V$. However, things went awry as I realised I didn't know the heat capacity of $\pu{HCl}$ nor did the exercise give it to me.


So, am I going about this the wrong way or am I just supposed to know the heat capacity of $\ce{HCl}$ off the top of my head?


