# Calculate the final temperature of the mixture

• JessicaHelena
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.
JessicaHelena

## 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.

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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.

## 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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