Enthelpy, heat of neutralization, calorimetry

[maxbashi]

Homework Statement

A quantity of 2.00x10^2 mL of .862 M HCl is mixed with 2.00x10^2 mL of .431 M Ba(OH)2 in a constant-pressure calorimeter of negligible heat capacity. The initial temperature of the HCl and Ba(OH)2 solutions is the same at 20.48 C.

For the process
H+(aq) + OH-(aq) --> H2O (l)
the heat of neutralization is -56.2 kJ/mol. What is the final temperature of the mixed solution?

Homework Equations

I'm thinking all I need is q=ms delta t

The Attempt at a Solution

q=(heat of neutralization per mol)(number of moles H2O)
q= -56.2 kJ/mol x (200 mL*.862mol/1000mL) = -9.69 kJ

If -9.69 = q = ms(T(f)-T(i))
Then T(f) = q/ms + T(i)
= -9690 J/(400g)(4.184g/J*C) + 20.48*C
= 121.8 degrees C

The answer should be 26.3 degrees C. Any help?

 

[Borek]

Do you know how to use calculator?

$$\frac{9690}{400\times4.184} + 20.48$$

and not

$$\frac{9690}{400} 4.184 + 20.48$$

(not to mention fact that you have lost minus sign, in a way luckily for you).

 

[maxbashi]

well that's embarrassing. thanks.

 

[Borek]

Happens

 

[DeeNos]

I would first commend you for showing your work and providing the necessary equations and information to solve the problem. Your approach is correct, however, there are a few mistakes in your calculations.

Firstly, the heat of neutralization is given in kJ/mol, so you need to convert it to J/mol by multiplying it by 1000.

Secondly, the number of moles of water formed should be the same for both the HCl and Ba(OH)2 solutions, so you should use the same volume (200 mL) and molarity (0.862 mol/L) for both solutions.

Finally, the specific heat capacity (s) should be for water, not the total mass of the solutions. So the correct value for s should be 4.184 J/g°C.

Correcting these mistakes, we get:

q = (-56.2 kJ/mol x 1000 J/kJ) x (200 mL x 0.862 mol/L) = -97.38 kJ

T(f) = -97.38 kJ / (200 mL x 0.862 mol/L x 4.184 J/g°C) + 20.48°C = 26.3°C

Therefore, the final temperature of the mixed solution is indeed 26.3°C. Great job on attempting the problem and keep up the good work!