What equation do I use for this problem?

Question

0.700 moles of an unknown solid is placed into water to make 150.0 mL of solution. The solution's temperature decreases by 5.51°C. Calculate ∆H, in kJ/mol, for the dissolution of the unknown solid. (The specific heat of the solution is 4.184 J/g･°C and the density of the solution is 1.02 g/mL).

Answer 1

The equation you are looking for is q = mC∆T

q = heat =?

m = mass of solution = 150.0 ml x 1.02 g / ml = 153 g

C = specific heat = 4.184 J/gº

∆T = change in temperature = 5.51º

q = (153 g)(4.184 J/gº)(5.51º)

q = 3527 J

On a per mole basis, we have...

3527 J / 0.700 mols = 5039 J / mole = 5.039 kJ / mol = -5.04 kJ /mol (3 sig figs) = ∆H

Since the temperature of solution DECREASED, this indicates the reaction is endothermic and hence ∆H has a negative sign.

Answer 2

The total heat lost during dissolution would be equal to the specific heat of solution times mass of solution times temperature change. We can divide this by the number of moles of dissolved substance to get the heat of dissolution.