Calculate the final temperature of the mixture

AI Thread Summary
The discussion revolves around calculating the final temperature of a mixture resulting from the reaction between HCl and Ba(OH)2. The initial calculations indicated that HCl was the limiting reactant, yielding 0.001382 moles, but there was confusion regarding the conversion of ΔH from kJ to J. Participants clarified that the heat released (Q) should be treated as positive due to the exothermic nature of the reaction, impacting the temperature calculation. The correct approach involved using the molarity and volume to find moles, leading to a revised final temperature of approximately 26.77°C. The discussion emphasizes the importance of using the correct formulas and units in thermodynamic calculations.
JessicaHelena
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Homework Statement


Consider the following reaction.
2 HCl(aq) + Ba(OH)2(aq)
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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.

Homework Equations


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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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?
 
JessicaHelena said:
.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)?
 
Looks much better.
 
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