A quantity of 85.0 mL of 0.900 M HCl is mixed with 85.0 mL of 0.900 M KOH in a constant-pressure calorimeter that has a heat capacity of 325 J/°C. If the initial temperature of both solutions are the same at 18.24°C, what is the final temperature of the mixed solution ?

The heat of neutralization is -56.2 kJ/mol.

Assume the density (1.00 g/mL) and the specific heat (4.184 J/g°C) of the solution is the same as those for water

Please help. thank u

## The heat of neutralization is

The heat of neutralization is -56.2 KJ/mol of reaction under investigation. The reaction under investigation is

1 H+ + 1 OH- ----> H2O (rxn 1)

comment: Cl- and K+ are spectator ions so didn't include them..

There is no limiting reagent (tagword) because the moles of HCl = moles NaOH (same volume and molarity mixed solutions)

So how much moles of reaction are reacting? There is 1 mole reaction per mole of H+ (or OH-). So moles reaction = moles of H+ (or OH-)..

moles H+ = moles HCl = .900 (moles/L) x 85.0 mL x 1/1000 (L/mL) = .0765 moles H+ = .0765 moles of reaction as written

So the quantity of heat released by the exothermic reaction = -56.2 KJ/mol x .0765 moles = - 4.30 KJ (this is part one)

So we know the reaction was exothermic released heat. So the water must warm up which is endothermic. Heat released by the chemical reaction (rxn 1).

We know the density, specific heat, and volume of water.

volume of water = 85.0 mL + 85.0 mL = 170 mL

the heat absorbed by water (raising its temperature) is equal to the heat released by the chemical reaciton!

heat absorbed by water = 170 mL x 1/1 (g/mL) x 4.184 (J/(g x degree C) x 1/1000 (KJ/J) x change in temperature = 4.30 KJ (from part one) (call this equation 1)

comment: for my brain it is easy to get the signs plus or minus wrong but I know the reaction releases heat and I know the water ends of warmer than it started just with common sense or 'chemistry sense'. So I ignore the sign for now and just calculate with respect to the quantity.

Ok so solving for change in termperature from equation 1 (above)

change in temperature (in degrees C) = 4.30 KJ x (1/4.184) ((g x degree C)/J) x 1000/1(J/KJ) x 1/1 (mL/g) x (1/170) (1/mL) = ?

change in temperature (in degrees C) = 6.05 degrees.

Comment: notice I ignored sign and next I will use reason to deduce the temperature increased so final temperature is 6.05 degrees higher than intial.

Comment: check yourself that 6.05 degrees seems within reason. Not 5000 degrees. Also check you got numerators and denominators right in solving for change in temperature. For example 170 mL should be a denominator because more water say a swimming pool would absorb more heat (though it would end up same because then at constant molarity there would be more moles of the reaction). Heat capacity is a denominator because things with big heat capacity by definition change less degrees for a given energy heat.

Answer = 6.05 + 18.24 = 24.29 degrees Celsius

Comment: I hope I didn't make a careless math error somewhere! And let me know if there is a question about where something I did is coming from. It's easy to make a math error. First I tried this I used 85 mL for volume instead of 170 mL.