Chemistry help please - on Enthalpy - for Higher coursework.?

Hello there, I have been doing a thing called enthalpy - I am good at it but there is a problem: I don't know how to do this one question!

"A polystyrene cup containes 50cm3 of water at 21.2*C.

2.53 g of of powdered ammonium chloride (NH4CL) was added and dissolved with stirring.

Calculate the lowest temperature which the solution should reach given that the enthalpy of solution of NH4CL is +15 KJ mol-1."

I know the answer is 17.8*C. BUT I don't know how to do the sum.

Can you help please help?

Just show me the how you worked it out.

Answer:
The first step is to convert the NH4Cl to moles. Divide the 2.53g by the molecular mass. Now multiply the moles by the enthalpy of solution of 15,000 J / mol.

This gives you the heat absorbed (it is endothermic) by the dissolving salt.

Now you have the total joules transfered.

The next formula for the water is q = m Cp delta T.

You already have the q. The Cp of water is 4.184 J / gram and your mass is 50 grams (1cm3 = 1 gram).

solve for the delta T and subtract it from the starting temp. of 21.2 C
OK...since the enthalpy of solution is positive, it means it's endothermic, so the energy must be supplied. The amount of energy is 15 kJ.mol-1

No of mol = mass / molar mass = 2.53 / 53.5 = 0.0473 mol

Enthalpy required = 15 * 0.0473 = 0.709 kJ = 709 J


Now...the energy will be supplied by loss of thermal energy of water, which can be expressed as mc(delta theta)

assuming density of water to be 1 g.cm-3, then mass of 50cm3 of water is 50g

So: 709 = 50*4.2*(delta theta) [where 4.2 Jg-1deg-1 is the specific heat capacity of water]

delta theta = 709 / 50*4.2 = 3.38 deg

So if starting T is 21.2 deg C, and water decreases in temperature to supply energy, final T will be 21.2 - 3.38 = 17.8 deg C.

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