Calculate the final temperature of the mixture

In summary, the given reaction is 2 HCl(aq) + Ba(OH)2(aq) → BaCl2(aq) + 2 H2O(l) with ΔH = -118 kJ. To 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, the limiting reactant is determined to be HCl and the final temperature of the mixture is calculated to be 26.7749 °C (ignoring sigfigs for now). The mistake in the initial attempt was not converting kJ to J and using the incorrect equation c=m/V instead of c=n/V.
  • #1
JessicaHelena
188
3

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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  • #2
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.
 
  • #3
@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?
 
  • #4
@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?
 
  • #5
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?
 
  • #6
@Borek
M means molar, which is concentration.
Oh the equation was in fact c= n/V, not m/V... right?
 
  • #7
@Borek
Would the answer then be 26.7749 °C (ignoring sigfigs for now)?
 
  • #8
Looks much better.
 

Related to Calculate the final temperature of the mixture

1. What is the equation for calculating the final temperature of a mixture?

The equation for calculating the final temperature of a mixture is: Tf = (m1 x T1 + m2 x T2) / (m1 + m2), where Tf is the final temperature, m1 and m2 are the masses of the two substances, and T1 and T2 are their initial temperatures.

2. What information do I need to calculate the final temperature of a mixture?

You need to know the masses and initial temperatures of the two substances being mixed, as well as the specific heat capacities of each substance.

3. How do you determine the specific heat capacity of a substance?

The specific heat capacity of a substance can be determined by performing a calorimetry experiment, where the amount of heat transferred to or from the substance is measured and used to calculate its specific heat capacity.

4. Can the final temperature of a mixture ever be lower than the initial temperatures?

No, the final temperature of a mixture can never be lower than the initial temperatures. The law of conservation of energy states that energy cannot be created or destroyed, only transferred. Therefore, in a closed system, the total energy of the substances before and after mixing must be equal, resulting in a final temperature that is equal to or higher than the initial temperatures.

5. Are there any assumptions made when calculating the final temperature of a mixture?

Yes, there are a few assumptions made when calculating the final temperature of a mixture. These include assuming that there is no heat loss to the surroundings, that the substances are well-mixed, and that no phase changes occur during the mixing process. These assumptions may not hold true in certain situations, leading to slightly different results.

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