Question

Which of the following will decrease the $pH$ of a $50\, ml$ solution of $0.01 \,M \,HCl$?

• A. addition of 5 ml of 1 M HCl
• B. addition of 50 ml of 0.01 M HCl
• C. addition of 50 ml of 0.002 M HCl
• D. addition of Mg

Answer 1

Answer: (D)

addition of Mg

Answer 2

Millimoles of $50 \,mL$ of $0.01 \,M HCl$
$=50 \times 0.01 \,M =0.5$
$pH$ of the solution $=-\log (0.5)=0.3010$
(a) On adding $5 \,mL$ of $1\, M\, HCl$, Concentration of the resultant solution
$=\frac{50 \times 0.01+5 \times 1}{50+5}=0.1$
$\therefore pH$ of the solution $=-\log (0.1)=1$
(b) On adding $50\, mL$ of $0.01 M \,HCl$,
Concentration of the resultant solution
$=\frac{50 \times 0.01+50 \times 0.01}{50+50}=0.01$
$\therefore pH$ of the solution $=-\log (0.01)=2$
(c) On adding $50\, mL$ of $0.002\, M\, HCl$,
concentration of the resultant solution
$=\frac{50 \times 0.01+50 \times 0.002}{50+50}=6 \times 10^{-3}$
$\therefore pH$ of the solution
$=-\log \left(6 \times 10^{-3}\right)=2.22$
(d) On adding $Mg$,
$Mg +2 HCl \longrightarrow MgCl _{2}+2 H ^{+}$
Since, $pH \propto \frac{ 1}{\left[ H ^{+}\right]}$
$\therefore$ In this case pH decreases.