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Question

The pH  of the solution obtained by mixing equal volumes of solution of $$pH=5$$ and $$pH=3$$ of the same electrolyte is:


A
3.3
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B
4.0
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C
4.5
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D
2.0
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Solution

The correct option is A $$3.3$$

Sample-1:
$$pH=5$$
$$pH=-log[H^+]=5$$
$$\Rightarrow [{ H }^{ + }]=10^ {-5}M = (M_1)$$
$$V_1=V_0$$

Sample2:
$$pH=3$$
$$pH=-log[H^+]=3$$
$$\Rightarrow [{ H }^{ + }]=10^ {-3}M = (M_2)$$
$$V_2=V_0$$

The concentration of the mixture of two solutions will be 

$$MV=M_1V_1+M_2V_2$$

$$M(V_0+V_0)=(10^{-5})V_0+(10^{-3})V_0$$

$$\Rightarrow M=\cfrac {10^{-5}+10^{-3}}{2}=0.000505$$

$$pH=-log[H^+]=-log(0.000505)=-(-3.29)=3.3$$

Chemistry

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