Enthalpy problem I do not understand A calorimeter is an insulated device in whi

Question

Enthalpy problem I do not understand

A calorimeter is an insulated device in which a chemical reaction is contained. By measuring the temperature change, Delta T, we can calculate the heat released or absorbed during the reaction using the following equation: q = specific heat times mass times Delta T Or, if the calorimeter has a predetermined heat capacity, C, the equation becomes q = C times Delta T At constant pressure, the enthalpy change for the reaction, Delta H, is equal to the heat, q_p; that is, Delta H = q_p 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, Delta E (sometimes referred to as Delta U), is the sum of heat, q, and work done, w: Delta E = q + w However, at constant volume (as with a bomb calorimeter) w = 0 and so Delta E = q_v. A calorimeter contains 33.0 mL of water at 15.0 degree C. When 2.30 g of X (a substance with a molar mass of 47.0 g/mol) is added, it dissolves via the reaction X(s) + H_2O(1) rightarrow X(aq) and the temperature of the solution increases to 28.5 degree C. Calculate the enthalpy change, Delta H, 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 middot degree 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 negative sign indicates an exothermic reaction in which heat is released and a positive sign indicates an endothermic reaction in which heat is absorbed. Since heat is released in this reaction, the sign of the enthalpy change must be negative.

Explanation / Answer

X(s) + H2O (l) <--> X(aq)

Moles of X = mass of X / Molar mass of X

         = 2.3 g / ( 47 g/mol)

      = 0.048936

water volume = 33 ml

mass of water = volume x density = 33 ml x 1g/ml = 33 g

solution mass = water mass + X mass = 33 g + 2.3 g = 35.3 g

Initial temperature of solution = 15 C

final temperature = 28.5 C

temperature rise = T2-T1 = 28.5 -15 = 13.5 C

Now heat absorbed by solution = specific heat of solution x mass of solution x temp rise

                  = 4.18 J/gC x 35.3 g x 13.5 C

             = 1992 J

This heat is given when X is dissolved in water

Per 0.048936 moles of X dissolved heat given is 1992 J

enthalphy per mole = - ( 1992 /0.048936) = - 40706 J/mol = - 40.7 KJ/mol

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