Calculate the molar enthalpy

Question

React 50.0 mL of 0.250 M sulfuric acid with 50.0 mL of 0.250 M potassium hydroxide in a bomb calorimeter. If the initial temperature of both reactants were 22.10oC and the final temperature of the solution was 25.26oC. If the calorimeter’s heat capacity was 5.17kJ/oC and assuming the density of the solution is 1.00g/mL. Calculate the molar enthalpy of this reaction

Answer 1

Caveat: a bomb calorimeter is usually used to find the heat of combustion and is under constant volume whereas molar enthalpy (∆H) is under constant pressure. With this caveat in mind, we will continue.

First thing to do is always write down the correctly balanced equation for the reaction:

H₂SO₄ + 2KOH ==> K₂SO₄ + 2H₂O .. balanced equation

Next, since they are asking us to find the molar enthalpy of reaction, we need to find the number of moles of each reactant, and then we will find the enthalpy, and finally, the molar enthalpy.

moles of H₂SO₄ = 50.0 mls H₂SO₄ x 0.250 mols / 1000 mls = 0.0125 mols H₂SO₄

moles KOH = 50.0 mls KOH x 0.250 mols / 1000 mls = 0.0125 mols KOH

Since it takes 2 moles KOH for each 1 mole of H₂SO₄ (see balanced equation), the KOH is limiting, which means 0.0125 moles of KOH will be used up and will react with 0.00625 moles of H₂SO₄ (2:1 mol ratio)

Now that we have determined moles of reactants, we can turn our attention to calculation the heat of the reaction that is taking place. For this we will use the following equation:

q = mC∆T + C_cal∆T

q = heat = ? (enthalpy)

m = mass of solution = 50.0 ml + 50.0 mls = 100. mls x 1 g / ml = 100. g

C = specific heat of solution = 4.184 J / gº (assuming the same specific heat as water)

∆T = change in temperature = 25.26º - 22.10º = 3.16º

C_cal = calorimeter constant = 5.17 kJ/º = 5170 J/º

Solving for q we have ...

q = (100 g)(4.184 J/gº)(3.16º) + (5170 J/º)(3.16º) = 1322 J + 16337 J

q = 17,659 J = 17.7 kJ

Now we have both moles of reactants and total heat, and so we can calculate molar heat of reaction:

molar heat of reaction = 17.7 kJ / 0.0125 mols = -1416 kJ / mole H₂O (negative since rxn is exothermic)