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A solution of 500 ml of 0.2 M KOH and 500 ml of 0.2M HCl is mixed and stirred, the rise in temperature is ${{T}_{1}}$. The experiment is repeated using 250 ml each of solution, the temperature rise is ${{T}_{2}}$, which of the following is true?
A) ${{T}_{1}} = {{T}_{2}}$
B) ${{T}_{1}} = 2{{T}_{2}}$
C) ${{T}_{1}} = 4{{T}_{2}}$
D) ${{T}_{2}} = 9{{T}_{1}}$

Last updated date: 21st Jun 2024
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Hint:. The temperature difference can be calculated using the equation, $Q = m{{C}_{V}}\Delta T$
- Where Q is the heat and n is the number of moles, ${{C}_{V}}$ is the specific heat capacity of a substance and $\Delta T$ is the change in temperature.

Complete step by step answer:
In the question, it is given than a solution of 500 ml of 0.2 M KOH and 500 ml of 0.2 M HCl is mixed and the temperature during the reaction is noted as ${{T}_{1}}$ and then another reaction is carried out by mixing 250 ml of KOH and 250 ml of HCl solution of 0.2 M and change in temperature can be calculated ie${{T}_{2}}$.
The reaction involved here is,
$KOH+HCl\to KCl+{{H}_{2}}O$
For finding the moles we can use the equation,
No. of moles =Molarity of the solution $\times$ Volume of the solution
Here the molarity of the solution is taken as 0.2 M as both the solutions have the same molarity and the volume of the solution is 500 ml.
No. of moles = 0.2 $\times$ 500 = 100
As in the question, ${{C}_{V}}$ is not given we eliminate the term and rewrite the equation as, $Q=n\Delta T$
For ${{Q}_{1}}$, ${{Q}_{1}} = n\Delta T = 100\times {{T}_{1}} = 100{{T}_{1}}$
Molarity of the solution is 0.2M and the volume of the solution is 250ml.
No. of moles = 0.2$\times$250 = 50
For${{Q}_{2}}$,${{Q}_{2}} = n\Delta T= 50\times {{T}_{2}} = 50{{T}_{2}}$
From the equations obtained we can say that the ${{Q}_{1}} = 2{{Q}_{2}}$
${{Q}_{1}} = 2{{Q}_{2}}$
$100{{T}_{1}} = 2\times 50{{T}_{2}}$
$100{{T}_{1}} = 100{{T}_{2}}$
${{T}_{1}} = {{T}_{2}}$
So, the correct answer is “Option A”.

Note: If mass is given in the question, then we can alter the equation as,$Q = m{{C}_{V}}\Delta T$
Where m is the mass of the substance given in the question.
- And for such problems the value for specific heat capacity of the substance ${{C}_{V}}$, will be provided in the question.