Question

A calorimeter contains 30.0 mL of water at 11.5 ∘C . When 2.10 g of X (a substance with a molar mass of 42.0 g/mol ) is added, it dissolves via the reaction

X(s)+H2O(l)→X(aq)

and the temperature of the solution increases to 30.0 ∘C .

Calculate the enthalpy change, ΔH, for this reaction per mole of X.

Assume that the specific heat of the resulting solution is equal to that of water [4.18 J/(g⋅∘C)], that density of water is 1.00 g/mL, and that no heat is lost to the calorimeter itself, nor to the surroundings.

Express the change in enthalpy in kilojoules per mole to three significant figures.

Answer 1

mass of water = density x volume = 30 x 1 = 30 g

total mass of solution = 30+ 2.10 = 32.10 g

dT = 30-11.5 = 18.5 oC

Q = m Cp dT

Q = 32.1 x 4.18 x 18.5 = 2482 J

Q = 2.482 kJ

moles of X = mass /molar mass

                 = 2.10 /42

               = 0.05

ΔH    = - Q / n

         = 2.482 / 0.05

          = - 49.6 kJ / mol