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
$S10 \ mL$ 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
    $P \rightarrow 1 ; Q \rightarrow 4 ; R \rightarrow 5 ; S \rightarrow 3$
  • D
    $P \rightarrow 1 ; Q \rightarrow 5 ; R \rightarrow 4 ; S \rightarrow 1$

Answer

 $\text { P: } \ce{CH_3COOH + NaOH} \longrightarrow \ce{CH_3COONa + H_2O}$
$20 ml$ of $0.1 m \ 10 ml$ of $0.1 m$
The value of  $H ^{+}$ does not change on dilution for buffer solution $P -(1)$
$\text {Q:} \ce{NaOH + CH_3COOH} \longrightarrow \ce{CH_3COONa + H_2O}$
$20 ml$ of $0.1 M \ 20 ml$ of $0.1 M$
$ C _1=0.05 M$
$C _2=0.025 M$  on dilution to $80 \ ml$
$M _1 V _1= M _2 V _2$
${\left[\left[ H ^{+}\right]=\frac{ K \omega}{\left[ OH ^{-}\right]}\right]}$
${\left[ OH ^{-}\right]=\sqrt{ K _{ n } C }=\sqrt{\frac{ K _{ e }}{ K _{ a }} \times C }}$
${\left[ H ^{+}\right]=\sqrt{\frac{ K _\omega \times K _{ a }}{ C }}}$
$\Rightarrow\left[ H ^{+}\right] \propto \frac{1}{\sqrt{ C }}$
$\frac{\left[ H _1^{+}\right]}{\left[ H _2^{+}\right]}=\sqrt{\frac{ C _2}{ C _1}}=\sqrt{\frac{0.025}{0.05}}$
$\frac{\left[ H _2^{+}\right]}{\left[ H _1^{+}\right]}=\sqrt{\frac{0.05}{0.025}}=\sqrt{2}$
${\left[ H _2^{+}\right]=\sqrt{2}\left[ H _1^{+}\right]}$
$R : \ce{NH_4OH + HCl} \longrightarrow \ce{NH_4Cl + H_2O}$
$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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