Which of the following when added to 20 mL of a 0.01 M solution of HCl would decrease its pH ?

Which of the following when added to 20 mL of a 0.01 M solution of HCl would decrease its pH ?
  1. 20 mL of 0.02 M HCl
  2. 20 mL of 0.005 M HCl
  3. 20 mL of 0.01 M HCl
  4. 40 mL of 0.005 M HCl

Solution

For an acid, pH of an acid solution will be lower as the solution is more concentrated. $\mathrm{pH}=-\log \left[\mathrm{H}^{+}\right]$
$\begin{aligned} & \mathrm{M}_{\mathrm{a}}=\frac{\mathrm{M}_1 \mathrm{~V}_1+\mathrm{M}_2 \mathrm{~V}_2}{\mathrm{~V}_1+\mathrm{V}_2} \\ &=\frac{2 \times 10^{-2} \times 10^{-2}+2 \times 10^{-2} \times 2 \times 10^{-2}}{4 \times 10^{-2}}=1.5 \times 10^{-2} \\ & \mathrm{M}_{\mathrm{b}}=\frac{2 \times 10^{-2} \times 10^{-2}+2 \times 10^{-2} \times 5 \times 10^{-3}}{4 \times 10^{-2}}=0.75 \times 10^{-2} \\ & \mathrm{M}_{\mathrm{c}}=\frac{2 \times 10^{-2} \times 10^{-2}+2 \times 10^{-2} \times 1 \times 10^{-2}}{4 \times 10^{-2}} \\ & \mathrm{M}_{\mathrm{c}}=1 \times 10^{-2} \\ & \mathrm{M}_{\mathrm{d}}=\frac{2 \times 10^{-2} \times 10^{-2}+4 \times 10^{-2} \times 5 \times 10^{-3}}{6 \times 10^{-2}} \\ &=\frac{4 \times 10^{-4}}{6 \times 10^{-2}} \\ & \mathrm{M}_{\mathrm{d}}=0.66 \times 10^{-2} \end{aligned}$
Order of concentration : $M_a \gt M_c \gt M_b \gt M_d$ Order of pH :- $\mathrm{M}_{\mathrm{d}} \gt \mathrm{M}_{\mathrm{b}} \gt \mathrm{M}_{\mathrm{c}} \gt \mathrm{M}_{\mathrm{a}}$ $\therefore \quad \mathrm{M}_{\mathrm{a}}$ have the lowest pH.

Asked in: AP EAMCET 2024 (22 May Shift 1)

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