Step 1 :The problem is asking to convert the units from Joules per millimole degree Celsius to kiloJoules per mole degree Celsius.
Step 2 :To do this, we need to know the conversion factors: 1 kJ = 1000 J and 1 mol = 1000 mmol.
Step 3 :So, the missing part of the equation should be the conversion factor that converts Joules to kiloJoules and millimoles to moles.
Step 4 :Therefore, the missing part of the equation should be \(\frac{1 \, \text{kJ}}{1000 \, \text{J}} \times \frac{1000 \, \text{mmol}}{1 \, \text{mol}}\).
Step 5 :Let's calculate the result of the equation with this conversion factor.
Step 6 :The result of the calculation is -67.0, which is in the unit of kJ/mol°C. This is the same unit as the one we want to convert to, so the conversion factor is correct.
Step 7 :Final Answer: The missing part of the equation is \(\boxed{\frac{1 \, \text{kJ}}{1000 \, \text{J}} \times \frac{1000 \, \text{mmol}}{1 \, \text{mol}}}\).