MCQ
Dilution processes of different aqueous solutions, with water, are given in LIST-I. The effects of dilution of the solutions on $\left[ H ^{+}\right]$are given in $LIST-II$.

(Note: Degree of dissociation ( $\alpha$ ) of weak acid and weak base is $<<1$; degree of hydrolysis of salt $<<1 ;\left[ H ^{+}\right]$represents the concentration of $H ^{+}$ions)

$LIST-I$ $LIST-II$

$P$ $(10 mL $of  $0.1 M NaOH +20 mL$ $of 0.1 M $  acetic acid) diluted to  $60 mL$

$1$ the value of $\left[ H ^{+}\right]$does not change on dilution

$Q $ $(20 mL $ of $ 0.1 M NaOH +20 mL $of $0.1 M $ acetic acid) diluted to $ 80 mL$

$2$ the value of $\left[ H ^{+}\right]$changes to half of its initial value on dilution the value of $\left[ H ^{+}\right]$changes to two times of its initial value on dilution

$R$ $(20 mL $ of $ 0.1 M HCl +20 mL$of $0.1 M$ ammonia solution) diluted to $80 mL$

$3$ the value of $\left[ H ^{+}\right]$changes to $1 / \sqrt{2}$ times of its initial value on dilution

$S$ $10 mL$ saturated solution of Ni $( OH )_2$in equilibrium with excess

solid  Ni $( OH )_2$ s diluted to  $20 mL$ (solid  Ni $( OH )_2$ is still present afterdilution).

$4$the value of $\left[ H ^{+}\right]$changes to $\sqrt{2}$ times of its initial value on dilution
  $5$ the value of $\left[ H ^{+}\right]$changes to $\sqrt{2}$ times of its initial value on dilution

Match each process given in $LIST-I$ with one or more effect(s) in $LIST-II$. The correct option is

  • A
    $P \rightarrow 4 ; Q \rightarrow 2 ; R \rightarrow 3 ; S \rightarrow 1$
  • B
    $P \rightarrow 4 ; Q \rightarrow 3 ; R \rightarrow 2 ; S \rightarrow 3$
  • C
    $P \rightarrow 1 ; Q \rightarrow 4 ; R \rightarrow 5 ; S \rightarrow 3$
  • $P \rightarrow 1 ; Q \rightarrow 5 ; R \rightarrow 4 ; S \rightarrow 1$

Answer

Correct option: D.
$P \rightarrow 1 ; Q \rightarrow 5 ; R \rightarrow 4 ; S \rightarrow 1$
d
$\begin{array}{l}\text { P: } \quad CH _3 COOH + NaOH \longrightarrow CH _3 COONa + H _2 O \\ 20 ml \text { of } 0.1 m \quad 10 ml \text { of } 0.1 m \\ \text { The value of } H ^{+} \text {does not change on dilution for buffer solution } P -(1) \text {. } \\ \text { Q: } NaOH + CH _3 COOH \longrightarrow CH _3 COONa + H _2 O \\ 20 ml \text { of } 0.1 M \quad 20 ml \text { of } 0.1 M \\\end{array}$

$\begin{array}{l} C _1=0.05 M \\ C _2=0.025 M \text { on dilution to } 80 ml \\ M _1 V _1= M _2 V _2 \\ {\left[\left[ H ^{+}\right]=\frac{ K \omega}{\left[ OH ^{-}\right]}\right]}\end{array}$

${\left[ OH ^{-}\right]=\sqrt{ K _{ n } C }=\sqrt{\frac{ K _{ e }}{ K _{ a }} \times C }}$

${\left[ H ^{+}\right]=\sqrt{\frac{ K _\omega \times K _{ a }}{ C }}}$

$\Rightarrow\left[ H ^{+}\right] \propto \frac{1}{\sqrt{ C }}$

$\frac{\left[ H _1^{+}\right]}{\left[ H _2^{+}\right]}=\sqrt{\frac{ C _2}{ C _1}}=\sqrt{\frac{0.025}{0.05}}$

$\frac{\left[ H _2^{+}\right]}{\left[ H _1^{+}\right]}=\sqrt{\frac{0.05}{0.025}}=\sqrt{2}$

${\left[ H _2^{+}\right]=\sqrt{2}\left[ H _1^{+}\right]}$

$R : NH _4 OH + HCl \longrightarrow NH _4 Cl + H _2 O$

$20 ml$ of $0.1 M 20 ml$ of $0.1 M$

$C _1=0.05 M$

$C _2=0.025 M$

${\left[ H ^{+}\right]=\sqrt{ K _{ n } C }}$

${\left[ H ^{+}\right] \propto \sqrt{ C }}$

${\left[ H _1^{+}\right]}$

${\left[ H _2^{+}\right]=\sqrt{\frac{ C _1}{ C _2}} \Rightarrow \frac{\left[ H _2^{+}\right]}{\left[ H _1^{+}\right]}=\sqrt{\frac{ C _2}{ C _1}}=\sqrt{\frac{0.025}{0.05}}=\sqrt{\frac{1}{2}}}$

${\left[ H _2^{+}\right]=\frac{1}{\sqrt{2}}\left[ H _1^{+}\right]}$

$R -(4)$

$S$ : The value of $\left[ H ^{+}\right]$does not change on dilution.

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