Chemistry Thermodynamics: The molar enthelpy of a solution

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Homework Statement

When 2.35 g of Mg(OH)2 is added to 250.0 mL of water, the temperature of the water raises from 20.5 degrees Celsius to 36.0 degrees Celsius. Calculate the molar enthalpy of the solution.

Relevant Equations

Q=mc ΔT

My answer is -0.40 kJ/mol. I'm having trouble understanding why the molar enthalpy of the solution is a negative number. Wouldn't this mean that the solution is losing energy? If the temperature of the water heats up from 20 degrees Celsius to 36 degrees Celsius shouldn't the final answer be positive? If the solution gains energy, that would heat up the water right?

I understand why the enthalpy of the system is negative, since it's being released from the system and into the solution, but why the solution is also a negative number confuses me.

 

[Chestermiller]

The enthalpy of solution at a given temperature is defined as the amount of heat you need to add to the solution to hold the temperature constant. Since the temperature in the test has risen, you would have had to remove heat in order to hold the temperature unchanged from its original value. So the heat of solution at 20 C is negative.

 

[mjc123]

I don't know what the exact wording of your question was, but I think you are looking for the "enthalpy of solution" (that is, of the process of dissolving), not the "enthalpy of the solution". The "system" is solid plus solvent (or solution once it's dissolved), not one or the other. The system releases energy; this would be released into the surroundings as heat if thermal transfer were perfectly efficient; as it isn't, the heat goes to raise the temperature of the solution.

Oh, and your answer is a factor of 1000 out. It should be -400 kJ/mol.