[Magh]

Question:
Aqueous silver ions reacts with aqueous chloride ion to yield a white precipitate of solid silver chloride. When 10.0 mL of a 1.00 M AgNO3 solution is added to 10.0 mL of a 1.00 M NaCl solution at 25°C in a calorimeter, a white precipitate of AgCl forms and the temperature of the aqueous mixture increases to 32.6°C. Assuming that the specific heat of the mixture is 4.18 J g-1 °C-1, that the density of the mixture is 1.00 g mL-1 and the calorimeter itself absorbs a negligible amount of heat, calculate ΔH (in kilojoules) for the reaction.
Solution:Moles AgCl formed = 0.01 L X 1 mol/L = 0.01 mol AgCl formed

Heat absorbed by solution during precipitation:
Mass of solution = 20 g (assuming density of 1.00)
q = m c (T2-T1) = 20 g (4.18 J/gC) (32.6 - 25.0) = 635 J

Since 635 J was absorbed by the solution, the reaction released -635 J

So

Delta H = -635 J/0.01 mol = -63500 J/mol = -63.5 kJ/mol
My question is why should I add the mass of agno3 and nacl solution because the 20g includes water which is the surrounding and water is not part of the reaction. The question is only asking for the heat absorbed by the water which is the heat release by the ag ion. Isn't the mass should only be the mass of the reaction?

[thetada]

The heat is not released from the silver ions but from the formation of bonds between the silver ions from the first solution and the chloride ions from the second solution. This heat is absorbed by all the water from both solutions, since they are now mixed. Hope this helps, I don't completely understand your question.

[Enthalpy]

Hi Magh, welcome!

The given data is consistent to my taste. You have the volumes of both solutions, not just water; the specific heat of the resulting mixture; the density of the mixture (or rather, ou supposed a density); and the released heat spreads over the whole mixture. Just fine - except that I expect a silver solution to be denser than water, and that pure water weighs 1000kg/m³ at +4°C only and rather 995 at RT.

One detail more: the reaction released +635J, that is, you put -635J in the equation.

Having computed the released heat by its effect on the complete mixture, you properly deduced how much a mole of Ag⁺ and Cl^- would release by precipitating. If the same amount of them were diluted in 10x more water, they would release the same amount of heat, which would raise the temperature 10x less (neglecting the heat capacity of the ions and precipitate).

Complications would arise at high concentration, when the ions interact, or even, when the concentration approaches the solubility limit. Then the heat of reaction departs from the one among dilute compounds. That's why tables give heat of solutes at 1M or at infinite dilution.