20 mL of calcium hydroxide was consumed when it was reacted with 10 mL of unknown solution of H2SO4. Also 20 mL standard solution of 0.5 M HCI containing 2 drops of phenolphthalein was titrated with calcium hydroxide the mixture showed pink colour when burette displayed the value of 35.5 mL whereas the burette showed 25.5 mL initially. The concentration of H2SO4 is ____ M (Nearest integer)
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Solution
Reaction with HCl
$$
\mathrm{Ca}(\mathrm{OH})_2+2 \mathrm{HCl} \rightarrow \mathrm{CaCl}_2+2 \mathrm{H}_2 \mathrm{O}
$$
Volume of $\mathrm{Ca}(\mathrm{OH})_2=10 \mathrm{ml}$
Volume of HCl $=20 \mathrm{ml}$
Concentration of $\mathrm{HCl}=0.5 \mathrm{M}$.
No. of milli moles of HCl = 10
No. of milli moles of $\mathrm{Ca}(\mathrm{OH})_2=5$
i.e., $\mathrm{M}_{\mathrm{Ca}(\mathrm{OH})_2}=\frac{\text { no. of milli moles }}{\mathrm{V}(\mathrm{ml})}=\frac{5}{10}=0.5 \mathrm{M}$
Reaction with $\mathrm{H}_2 \mathrm{SO}_4$
$\mathrm{Ca}(\mathrm{OH})_2+\mathrm{H}_2 \mathrm{SO}_4 \rightarrow \mathrm{CaSO}_4+2 \mathrm{H}_2 \mathrm{O}$
No. of milli moles of $\mathrm{Ca}(\mathrm{OH})_2=20 \times 0.5=10$ i.e., no. of milli moles of $\mathrm{H}_2 \mathrm{SO}_4=10$
$$
\Rightarrow \mathrm{M}_{\mathrm{H}_2 \mathrm{SO}_4}=\frac{\text { no. of milli moles }}{\mathrm{V}(\mathrm{ml})}=\frac{10}{10}=1 \mathrm{M}
$$
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