In a constant‑pressure calorimeter, 50.0 mL of 0.300 M Ba(OH)2 was added to 50 mL of 0.600 M HCl.

Question

The reaction caused the temperature of the solution to rise from 22.54 to 26.63 ∘C. If the solution has the same density and specific heat as water, what is the heat absorbed by the solution?

Assume that the total volume is the sum of the individual volumes. (And notice that the answer is in kJ).

Answer 1

As with all thermochemical problems, it is helpful to define system and surroundings here. By the law of conservation of energy, any heat lost by the system is absorbed by the surroundings. In this case, your system would be your chemical reaction between Ba(OH)₂ and HCl and the surroundings would be the solution, which is mostly water. Hence you may assume that the specific heat capacity of the solution (or the amount of heat required to raise the temperature of 1 gram of it by 1 degree Celsius) is the same as that of water: 4.186 Joules/(g-^oC)

The law of conservation of energy can be written:

Heat (q) gained by surroundings (or solution) = - heat lost by the system (or reaction)

Given the change in temperature of the solution, and its mass, you can calculate the heat it absorbed with the equation:

q = mCΔT, where q= heat, m= mass of the solution, C is its heat capacity and ΔT is the change in temperature.

The mass of the solution can be obtained by adding the volumes of the two solutions: 50.0 mL HCl + 50.0 mL Ba(OH)₂ = 100 mL total, and multiplying that by the

density of water = 1.00 g/ mL, so the mass would be simply 100 g.

ΔT = T_final – T_initial = 26.63 -22.54 ^oC = 4.09 ^oC

Plugging the mass, heat capacity and change in temperature into the equation for q, you get

q = (100 g)(4.186 J/(g- deg C)(4.09 deg C) = 1712 J 

Notice that all units cancel out except for Joules which is a unit of energy, so this is a good way to evaluate if your answer is likely to be right. The problem asks for the answer in kJ. There are 1000 J/kJ. I will leave the conversion of the 1712 J to kJ for you to do.