A13.1-g sample of cacl2 is dissolved in 104 g of water, with both substances at 24.7°c. calculate the final temperature of the solution assuming no heat loss to the surroundings and assuming the solution has a specific heat capacity of 4.18 j °c−1 g−1.

The final temperature of the solution is 44.8 °C

Explanation:

assuming no heat loss to the surroundings, all the heat of solution (due to the dissolving process) is absorbed by the same solution and therefore:

Q dis + Q sol = 0

Using tables , can be found that the heat of solution of CaCl2 at 25°C (≈24.7 °C)  is q dis= -83.3 KJ/mol . And the molecular weight is

M = 1*40 g/mol + 2* 35.45 g/mol = 110.9 g/mol

Q dis = q dis * n  = q dis * m/M =  -83.3 KJ/mol * 13.1 g/110.9 gr/mol = -9.84 KJ

Qdis= -9.84 KJ

Also Qsol = ms * Cs * (T - Ti)

therefore

ms * Cs * (T - Ti) + Qdis = 0

T=  Ti - Qdis * (ms * Cs )^-1   =24.7 °C - (-9.84 KJ/mol)/[(104 g + 13.1 g)* 4.18 J/g°C] *1000 J/KJ

T= 44.8 °C