Well, it seems like we've got some chemistry equations here. Let's see if I can lighten things up a bit!
To find the heat capacity of the calorimeter, we can use the equation:
q = C × ΔT
Where q is the heat absorbed or released, C is the heat capacity, and ΔT is the change in temperature.
We already know that the temperature change (ΔT) is 29.1 °C - 22.0 °C = 7.1 °C. But we still need to find the heat (q) absorbed by the solution.
To find q, we can use the formula:
q = m × c × ΔT
Where m is the mass of the solution and c is its specific heat capacity.
We know that the mass of the solution is 28.00 g. And the specific heat capacity (c) is 3.74 J K-1 g-1. So let's plug in those numbers:
q = (28.00 g) × (3.74 J K-1 g-1) × (7.1 °C)
Now we have the heat (q) absorbed by the solution. But remember, energy is conserved, so the heat absorbed by the solution is equal to the heat released by the calorimeter, which is equal to the heat absorbed by the system (the 15.0 mL of NaOH and 13.0 mL of HCl).
So, we can set up the equation:
q = C_calorimeter × ΔT
Where C_calorimeter is the heat capacity of the calorimeter.
Therefore, we can rearrange the equation to solve for C_calorimeter:
C_calorimeter = q / ΔT
Now, let's plug in the values we found for q and ΔT:
C_calorimeter = (28.00 g × 3.74 J K-1 g-1 × 7.1 °C) / 7.1 °C
Simplifying, we find:
C_calorimeter = 28.00 g × 3.74 J K-1 g-1 = 104.72 J/°C
So, the heat capacity of the calorimeter is 104.72 J/°C.
Now, as for the molar enthalpy of neutralization per mole of HCl being -55.84 kJ mol-1, well, that's a bit of a serious number. But hey, at least it's negative, right? Let's just say it's one way chemistry can be a bit of a downer!