Question

A calorimeter contains 17.0 mL of water at 11.5 ∘C . When 1.60 g of X (a substance with a molar mass of 79.0 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

We know for a calorimeter

q = m C_p ΔT

17.0 mL water will be 17.0 x 10 g /mL = 17 g

when we are adding 1.6 g of X the total weight in the calorimeter will be 17g + 1.6 g = 18.6 g

q = 18.6 g x 4.18 J/(g⋅∘C) x (30.0 - 11.5)^∘C

q = 18.6 g x 4.18 J/(g⋅^∘C) x 18.5^∘C

q = 1438.3 J

1.6 g of X has molar mass of 79.0 g/mol

so number of moles is 1.6g/79.0 g/mol = 0.0202 moles

- H = q/moles = 1438.3 J/0.0202 moles = 71016.0 J

H = -71.016 kJ/mole