Question

A 0.249g pellet of potassium hydroxide, KOH, is added to 64.0g water in a Styrofoam coffee cup. The water temperature rises from 23.5 to 24.4 ?C. [Assume that the specific heat of dilute KOH(aq)is the same as that of water.] What is the approximate heat of solution of KOH, expressed as kilojoules per mole of KOH?

Answer 1

q = m*Cp*(T2-T1), where q is the heat gained by the substance, m is the mass of the substance, Cp is the substance's specific heat, and (T2-T1) is the change in temperature of that substance (final temperature - initial temperature).

The other thing that you have to understand is that all of the heat given off by the salt (i.e. KOH) as it dissolves will be gained by the water, so q(water) = -q(salt). (By convention, heat that is given off will be a negative value. You may also see this equation with ?H instead of q; for purposes of these problems, they mean the same thing (you'll learn the difference if you take more chemistry later on).

The first step for a problem like this is to calculate the amount of heat gained by the water using the equation above. To do this, you need to know the specific heat of the solution. The problem tells you to assume that this is the same as the specific heat of water (4.186 J/g*degree C). The problem tells you that the mass of the water is 64 g and the temperature change is (24.4 - 23.5) degrees C = 0.9 degrees C. Plugging all of these values into the equation:

q(water) = (64.0 g)(4.186 J/g*degree C) (0.9 degrees C)
q(water) = 241.11 J

Now, remember that q(salt) = -q(water):
q(KOH) = -241.11J

This is the amount of heat given off by dissolving .249 g KOH. But you have to express your answer in kJ/mol! To do this, you first have to find the number of moles of KOH. The molar mass of KOH is (39.10 g/mol) + (16.00 g/mol) + (1.008 g/mol) = 56.108 g/mol. Therefore, the number of moles of KOH that dissolved is just the mass that dissolved divided by this molar mass.

0.249 g KOH * (1 mol / 56.108 g) = 0.0044 moles KOH.

To find the heat released per mole of KOH, divide the heat released--that's q(KOH)--by the number of moles:

q(KOH)/moles = -241.11J / 0.0044 mol = -54797.72J/mol

Now, all that's left is to convert J to kJ by multiplying by 1 kJ / 1000 J:

= -54797.7273J/mol * (1 kJ / 1000 J)

= -54.79 kJ/mol = the heat of solution of KOH expressed in kJ/mol