$20 \mathrm{mL}$ of a mixed solution of ${\mathrm{Na}}_2{\mathrm{CO}}_3$ and $\mathrm{NaOH}$ required $17.5 \mathrm{mL}$ of $\frac{\mathrm{N}}{10} \mathrm{HCl}$ when titrated with phenolphthalein as indicator. But when methyl orange was added, a second endpoint was observed on further addition of $2.5 \mathrm{mL}$ of $\mathrm{HCl}$. Calculate the amount of ${\mathrm{Na}}_2{\mathrm{CO}}_3$ and $\mathrm{NaOH}$ in the solution. 

A sample of hydrazine sulphate $\left({\mathrm{N}}_2{\mathrm{H}}_4{\mathrm{SO}}_4\right)$  was dissolved in $100 \mathrm{mL}$ of water. $10 \mathrm{mL}$ of this solution was reacted with excess of ferric chloride solution and warmed to complete the reaction. Ferrous ion formed was estimated and it required $20 \mathrm{mL}$ of $\mathrm{M}/50$ potassium permanganate solution. Estimate the amount of hydrazine sulphate in one litre of the solution. Reactions:

$4{\mathrm{Fe}}^{+++}+{\mathrm{N}}_2{\mathrm{H}}_4\to {\mathrm{N}}_2+4{\mathrm{Fe}}^{++}+4{\mathrm{H}}^{+}$

${\mathrm{MnO}}_4^{-}+5{\mathrm{Fe}}^{++}+8{\mathrm{H}}^{+}\to {\mathrm{Mn}}^{++}+5{\mathrm{Fe}}^{+++}+4{\mathrm{H}}_2\mathrm{O}$

A $10 \mathrm{g}$ mixture of ${\mathrm{Cu}}_2\mathrm{S}$ and $\mathrm{CuS}$ was treated with $200 \mathrm{mL}$ of $0.75 \mathrm{M} {\mathrm{MnO}}_4^{-}$ in acid solution producing ${\mathrm{SO}}_2, {\mathrm{Cu}}^{2+}$ and ${\mathrm{Mn}}^{2+}$. The ${\mathrm{SO}}_2$ was boiled off and the excess ${\mathrm{MnO}}_4^{-}$ was titrated with $175 \mathrm{mL}$ of $1 \mathrm{M} {\mathrm{Fe}}^{2+}$ solution. Calculate the percentage of $\mathrm{CuS}$ in the original mixture.

A $0.518 \mathrm{g}$ sample of limestone is dissolved and then, $\mathrm{Ca}$ is precipitated as ${\mathrm{CaC}}_2{\mathrm{O}}_4$. After filtering and washing the precipitate, it requires $40 \mathrm{mL}$ of $0.25 \mathrm{N}$ ${\mathrm{KMnO}}_4$ solution acidified with ${\mathrm{H}}_2{\mathrm{SO}}_4$ to titrate it. What is the percentage of $\mathrm{CaO}$ in limestone?

${\mathrm{MnO}}_4^{-}+{\mathrm{CaC}}_2{\mathrm{O}}_4+{\mathrm{H}}_2{\mathrm{SO}}_4\to {\mathrm{CaSO}}_4+{\mathrm{Mn}}^{2+}+{\mathrm{CO}}_2+{\mathrm{H}}_2\mathrm{O}$

$20 \mathrm{mL}$ of $\frac{\mathrm{M}}{60}$ solution of ${\mathrm{KBrO}}_3$ was added to a certain volume of ${\mathrm{SeO}}_3^{2-}$ solution. ${\mathrm{Br}}_2$ evolved was removed by boiling and the excess of ${\mathrm{KBrO}}_3$ was back titrated with $5.1 \mathrm{mL}$ of $\frac{\mathrm{M}}{25}$ solution of ${\mathrm{NaAsO}}_2$. Calculate the weight of ${\mathrm{SeO}}_3^{2-}$ in the solution.

give the answer up to three places of decimal.

Concentrated $\mathrm{HCl}$ solution is $37.0\% \mathrm{HCl}$ and has a density of $1.19 \mathrm{g} {\mathrm{mL}}^{-1}$. A dilute solution of $\mathrm{HCl}$ is prepared by diluting $4.50 \mathrm{mL}$ of this concentrated $\mathrm{HCl}$ solution to $100 \mathrm{mL}$ with water. Then, $10 \mathrm{mL}$ of this dilute $\mathrm{HCl}$ solution reacts with an ${\mathrm{AgNO}}_3$ solution. Calculate the volume of $0.108 \mathrm{M} {\mathrm{AgNO}}_3$ solution required to precipitate all the chloride as $\mathrm{AgCl}\left(\mathrm{s}\right)$.

Give the answer up to two decimal places.