Question

PLEASE SHOW COMPLETE AND CLEAR SOLUTION thanks.

A 51.6-mL dilute solution of acid at 23.85°C is mixed with 48.5 mL of a dilute solution of base, also at 23.85°C, in a coffee-cup calorimeter. After the reaction occurs, the temperature of the resulting mixture is 27.25°C. The density of the final solution is 1.03 g/mL. Calculate the amount of heat evolved. Assume the specific heat of the solution is 4.184 J/g•°C. The heat capacity of the calorimeter is 23.9 J/°C.

Answer 1

Solution :-

Volume of acid solution =51.6 ml

Volume of base solution =48.5 ml

Density of the solution =1.03 g/ml

Initial temperature =23.85 C

Final temperature = 27.25 C

Specific heat of solution = 4.184 J/gC

Heat capacity of the calorimeter =23.9 J/C

Heat evolved = ?

Volume of mixture = 51.6 ml + 48.5 ml = 100.1 ml

Mass of mixture = volume * density

                              = 100.1 ml * 1.03 g /ml

                            = 103.1 g

The energy produced from the reaction is absorbed by the solution to rise in temperature also some of energy is absorbed by the calorimeter therefore to calculate the total energy evolved we can make the following set up

q total = q cal + q solution

q total = (c cal * delta T)+(m*c*delta T)

delta T= T2-T1 = (27.25C -23.85C) =3.4C

q total = (c cal * delta T)+(m*c*delta T)

             = (23.9 J per C* 3.4C)+(103.1 g* 4.184 J per g C *3.4 c)

            = 81 +1465 J

            = 1546 J

1546 J * 1 kJ / 1000 J = 1.546 kJ

Therefore total amount of heat evolved = 1.546 kJ or 1546 J