50.0 mL of a solution of HCl is combined with 100.0 mL of 1.05M NaOH in a calori

Question

50.0 mL of a solution of HCl is combined with 100.0 mL of 1.05M NaOH in a calorimeter. The reaction mixture is initially at 22.4 degree C, and the final temperature after reaction is 30.2 degree C. What is the molarity of the HCl solution? You may assume that there is an excess of base (so that all the HCl has reacted), that the specific heat of the reaction mixture is 0.96 cal/g degree C, and that the density of the reaction mixture is 1.02 g/mL. The heat of neutralization of HC1 and NaOH is 13.6 kcal/mole.

Explanation / Answer

Solution.

The total volume of the solution is 100+50=150 mL; the mass of the final reaction mixture is 150*1.02 = 153 g.

The amount of neutralization heat released is q = 0.96*153*(30.2-22.4)= 1146 cal.

When one mole of HCl was neutralized, 13600 cal of heat releases. As the amount of heat released is proportional to the amount of substance, the amount of HCl is n(HCl)=1146/13600=0.084 mol.

The concentration is a ratio of amount of substance to a volume of solution:

c = n/V = 0.084/0.150=0.562 M.

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