# Calculate the final temperature of the mixture

## Homework Statement

Consider the following reaction.
2 HCl(aq) + Ba(OH)2(aq)
BaCl2(aq) + 2 H2O(l) ΔH = -118 kJ
Calculate the heat when 100.8 mL of 0.500 M HCl is mixed with 300.0 mL of 0.450 M Ba(OH)2. Assuming that the temperature of both solutions was initially 25.0°C and that the final mixture has a mass of 400.8 g and a specific heat capacity of 4.18 J/°C · g, calculate the final temperature of the mixture.

Q=mc(delta)T
c=m/V

## The Attempt at a Solution

using c=m/V and that n = m/M, I got that HCl is the Limiting Reactant and that there are 0.001382 moles of it. Then Q = delta H = -118*0.001382/2 = -0.081538
Plugging this into Q=mc(delta)T:
-0.081538 = 400.8 x 4.18 x (T_f - 25)
I got T_f = 24.99..., which is wrong.

Where did I go wrong? My assignment is due soon, so please help!

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## Answers and Replies

mjc123
Homework Helper
Where do you get 0.001382 moles from?
You have failed to convert kJ into J.
Negative ΔH means heat is given out, so that raises the temperature - Q in Q = mcΔT should be positive.

@mjc123
.1008L x 0.5 M = 0.0504 g
and since the molar mass of HCl is (35.45 + 1.008)g/mol, doing 0.0504/(35.45+1.008) = 0.001382
am I doing it wrong?

@mjc123 I tried to convert kJ into J (supposing the moles is right above), but for some reason, I get a similar answer — 25.0487 — but is this right?

Borek
Mentor
.1008L x 0.5 M = 0.0504 g

No, that's not how it works. You don't have 0.0504 g o the substance.

What does 'M' mean in the context of the concentration?

@Borek
M means molar, which is concentration.
Oh the equation was in fact c= n/V, not m/V... right?

@Borek
Would the answer then be 26.7749 °C (ignoring sigfigs for now)?

Borek
Mentor
Looks much better.