Question

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2. Two solutions namely, 500 mL of 0.50 M HCl and 500 mL of 0.50 M NaOH at the same temperature of 21.6 °C are mixed in a constant-pressure calorimeter. The heat capacity of the calorimeter was 450 J/oC. Given that the specific heat of the solution is 4.184 J/g°C, the density of the solution is 1.00 g/mL, and that the heat of neutralization for the process H* (aq) + OH (aq) -- H2O (1) is -56.2 kJ, what is the final temperature of the mixed solution?

Answer 1

Number of HCl , n = Molarity * Volume in L

                           = 0.50M * 500mL*10^-3L/mL

                           = 0.25 moles

Number of NaOH , n' = Molarity * Volume in L

                          = 0.50M * 500mL*10^-3L/mL

                           = 0.25 moles

Total volume of the solution , V = 500mL+500 mL = 1000 mL

So mass of solution , m = Volume * density of solution

                                   = 500 mL * 1.00 g/mL

                                   = 500 g

Given heat of neutralization of solution for 1 mole of HCl is -56.2 kJ

For 0.25 moles of HCl the heat of neutralization is 0.25 mole * (-56.2kJ) = -14.05 kJ = -14050 J

c = specific heat capacity of solution = 4.184J/goC

So heat lost by solution , Q = Ldt + mcdt

Where m = mass of solution = 500g

       c = specific heat capacity of solution = 4.184 J/goC

       dt = change in temperature = t - 21.6 oC

      L = heat capacity of calorimeter = 450 J/oC

Plug the values we get dt (L+mc) = Q

                                   dt = Q / (L + mc )

                                      = 14050 J / [450 +(500*4.184)]

                                      = 5.53 oC

                           t - 21.6 = 5.53

                                   t = 27.13 oC

Therefore the final temperature of the solution is 27.13 oC