A calorimeter contains 35.0 mL of water at 14.0 °C. When 1.40 g of X (a substance with a molar mass of 43.0 g/mol) is added, it dissolves via the reaction
X(s) + H2O(l) → X(aq)
and the temperature of the solution increases to 29.0°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.
A calorimeter is an insulated device in which a chemical reaction is contained. By measuring the temperature change, ΔT, we can calculate the heat released or absorbed during the reaction using the following equation:
q = specific heat × mass × ΔT
Or, if the calorimeter has a predetermined heat capacity, C, the equation becomes
q = C × ΔT.
At constant pressure, the enthalpy change for the reaction, ΔH, is equal to the heat, qp; that is,
ΔH = qp
but it is usually expressed per mole of reactant and with a sign opposite to that of q for the surroundings. The total internal energy change, ΔE (sometimes referred to as ΔU), is the sum of heat, q, and work done, w:
ΔE = q + w
However, at constant volume (as with a bomb calorimeter) w = 0 and so ΔE = qv.
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