Temperature of chlorine gas at given pressure and volume
Assuming at these conditions it's safe to use ideal gas law ($pV = nRT$) for chlorine, and given the same gas sample ($n = \text{const}$, hence $nR = \text{const}$), let's express the unknown temperature $T_2$:

$$\frac{p_1V_1}{T_1} = \frac{p_2V_2}{T_2} \quad \to \quad T_2 = \frac{p_2V_2}{p_1V_1} \cdot T_1$$

Generally, I would recommend not to do intermediate calculations, especially if you are not asked to do so. Construct the mathematical expression first, convert the units if necessary, and plug in the values when you are done. Note that in this case you only need to convert temperature units.


   $$T_2 = \frac{\pu{876 torr} \cdot \pu{15.00 L}}{\pu{1124 torr} \cdot \pu{9.22 L}} \cdot \pu{297 K} = \pu{377 K}~\text{or}~\pu{104 ^\circ C}$$