Calculating the heat capacity of a calorimeter
$12.5\ \mathrm{kJ}$ of heat was absorbed by the surroundings.

I found this by using the mcat formula and the specific heat capacity of water (4.18 J/(g °C)):

$Q=m\cdot c\cdot\Delta T$

$Q = 950\ \mathrm{g} \times (4.18\ \mathrm{J\cdot g^{-1}\cdot {^\circ C^{-1}}}) \times (23.25\ \mathrm{^\circ C} - 20.10\ \mathrm{^\circ C}) = 12508.7\ \mathrm{J}$

If you wanted to use this whole formula for solving the calorimeter's specific heat capacity, you would need to know the mass of the calorimeter as well, which is not given.

What your book is probably asking is for what is called the "calorimeter constant". This is given in units of $\pu{J/^\circ C}$ notice that it does not include mass.



Note: Sometimes "the calorimeter's specific heat capcity" is used instead of referring to the calorimeter constant, but in this case we cannot find a value which will include mass in the units, so I think it is more clear to use the term "calorimeter constant."



You can determine the constant by this formula: $$Q_\text{cal} = C_\text{cal} \times \Delta T_\text{cal}$$

Where $Q_\text{cal}$ is the energy absorbed, $C$ is the constant and $\Delta T$ is the same as the change in temperature of the water.

You may calculate $Q_\text{cal}$ by using this formula: $$Q_\text{cal} = -(Q_\text{water} + Q_\text{glucose})$$

It may also help to think of $Q_\text{water}$ = $Q_\text{surroundings}$ and $Q_\text{glucose}$ = $Q_\text{system}$

To find $Q_\text{glucose}$ I did: (glucose has lost energy, it is negative value)

$-2820\ \mathrm{kJ} \times 0.007\ \mathrm{mol}$ and $Q_\text{water}$ is simply the $12508.7\ \mathrm{J}$ positive because $\Delta T$ is positive for the surroundings (the system/glucose lost energy)

$Q_\text{cal} = -(12508.7\ \mathrm{J} + (-19740\ \mathrm{J}))$

So my final answer is then: $2.3\times10^3\ \mathrm{J/{^\circ C}}$

It is important that heat capacities are positive, think about what it would mean if this were a negative value.



In the laboratory, it is necessary to do a calculation such as this one before using a calorimeter for anything. Normally it can be done by heating a piece of nickel or something, recording the temperature of the metal and the water, and then dropping the metal into the calorimeter to find the final temperatures, and then calculate the calorimeter constant. You can then proceed with further experimentation using that calorimeter, but only after this constant has been found can you find the specific heat capacity of other materials.