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Question

Answers

A. x

B. $\dfrac{x}{2}$

C.$\dfrac{x}{4}$

D.$\dfrac{{2x}}{3}$

Answer
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$ \Rightarrow {\text{No}}{\text{. of gram equivalent = N}} \times {\text{V}}$

Where N is the normality and V is the volume of solution in litres.

Normality of $HCl$=$2$ and Volume = $500$ ml$ = \dfrac{{500}}{{1000}}$ litres.

And Normality of $NaOH$=$4$ and volume =$250$ml= $\dfrac{{250}}{{1000}}$ litres.

We have to find the heat of neutralization when these two solutions are mixed.

We know that the heat of neutralization is equal to the enthalpy change of reaction when one gram equivalent of acid is neutralized by one gram equivalent of base.

Here $HCl$ is acid and $NaOH$ is base. So we have to find the number of gram equivalents of both.

We know that

$ \Rightarrow {\text{No}}{\text{. of gram equivalent = N}} \times {\text{V}}$

Where N is the normality and V is the volume of solution in litres.

Then No. of gram equivalents of $HCl$= ${\text{Normality of HCl}} \times {\text{Volume of acid}}$

On putting the given values we get,

$ \Rightarrow {\text{No}}{\text{. of gram equivalents of HCl}} = \;2 \times \dfrac{{500}}{{1000}}$

On simplifying we get,

\[ \Rightarrow {\text{No}}{\text{. of gram equivalents of HCl}} = \;\dfrac{{1000}}{{1000}} = 1\]

Now, No. of gram equivalents of $NaOH$= ${\text{Normality of NaOH}} \times {\text{Volume of base}}$

On putting the given values we get,

$ \Rightarrow $ No. of gram equivalents of $NaOH = 4 \times \dfrac{{250}}{{1000}}$

On simplifying we get,

$ \Rightarrow $ No. of gram equivalents of $NaOH = \dfrac{{1000}}{{1000}} = 1$

Since here one gram equivalent of acid is neutralized by one gram equivalent of base then,

Heat evolved= Enthalpy of neutralization

And we know that enthalpy of neutralization of $HCl$ and $NaOH$ is x KJ

∴Heat evolved= x KJ

Number of gram equivalent can also be expressed by this formula-

$ \Rightarrow {\text{No}}{\text{. of gram equivalent = }}\dfrac{{{\text{Weight of solute}}}}{{{\text{Equivalent weight of solute}}}}$

Equivalent weight is calculated by dividing the molecular weight by the charge number. Charge number is the number of protons or hydroxide which the compound contains.

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