Question

Consider the titration curve in exercise $\mathbf{91}$for the titration of ${\mathbf{Na}}_2{\mathbf{CO}}_3$with $\mathbf{HCl}$

1. If a mixture of ${\mathbf{NaHCO}}_3\mathbf{and}{\mathbf{Na}}_2{\mathbf{CO}}_3$was titrated, what would be the relative sizes ofrole="math" localid="1657957423543" ${\mathbf{V}}_1\mathbf{and}{\mathbf{V}}_2$ ?
2. If a mixture of $\mathbf{NaOH}\mathbf{and}{\mathbf{Na}}_2{\mathbf{CO}}_3$was titrated, what would be the relative sizes of ${\mathbf{V}}_1\mathbf{and}{\mathbf{V}}_2$?
3. A sample contains a mixture of ${\mathbf{NaHCO}}_3\mathbf{and}{\mathbf{Na}}_2{\mathbf{CO}}_3$, when this sample was titrated with $\mathbf{0}\mathbf{.}\mathbf{100}\mathbf{M}\mathbf{HCl}$, it took$\mathbf{18}\mathbf{.}\mathbf{9}\mathbf{mL}$ to reach the first stoichiometric point and an additional$\mathbf{36}\mathbf{.}\mathbf{7}\mathbf{mL}$ to reach the second stoichiometric point. What is the composition in mass percent of the sample?

Short answer

1. ${\text{V}}_{\text{2}}>{\text{V}}_1$
2. ${\text{V}}_1>{\text{V}}_2$
   
3. Percentage mass of ${\text{Na}}_{\text{2}}{\text{CO}}_{\text{3}}$is$57.14\%$

Percentage mass of${\text{NaHCO}}_{\text{3}}$ is$42.86\mathrm{\%}$

Step-by-step solution

Definition of titration

The process of adding the standard solution to the solution of unknown concentration until the reaction is just completeis defined as titration.

Find the greater volume

a.

${\mathrm{V}}_1$is the volume of acid required for the titration of${\text{Na}}_{\text{2}}{\text{CO}}_{\text{3}}$with ${\text{H}}^{\text{+}}$

${\mathrm{V}}_2$is the volume of acid required for the titration of${{\text{HCO}}_{\text{3}}}^{-}$with ${\text{H}}^{\text{+}}$

There are two sources of ${{\text{HCO}}_{\text{3}}}^{-}$which is present and produced after the first equivalence point of the titration of${\text{Na}}_{\text{2}}{\text{CO}}_{\text{3}}$

So ${\text{V}}_{\text{2}}>{\text{V}}_1$

b.

${\mathrm{V}}_1$is the volume of acid required for the titration of $\text{NaOH}$and the titration of ${\text{Na}}_{\text{2}}{\text{CO}}_{\text{3}}$.

${\mathrm{V}}_2$ is the volume of acid required for the titration of ${{\text{HCO}}_{\text{3}}}^{-}$produced from the titration of role="math" ${\text{Na}}_{\text{2}}{\text{CO}}_{\text{3}}$.

So ${\text{V}}_1>{\text{V}}_2$

c.

Mass of ${\text{Na}}_{\text{2}}{\text{CO}}_{\text{3}}$ present $=0.200\text{\hspace{0.17em}g}$

Mass of${\text{NaHCO}}_{\text{3}}$ present$=0.15\text{\hspace{0.17em}g}$

Percentage mass of ${\text{Na}}_{\text{2}}{\text{CO}}_{\text{3}}$$=\frac{0.2\text{\hspace{0.17em}g}}{0.2\text{\hspace{0.17em}g}+0.15\text{g}}\times 100\mathrm{\%}$

$=57.14\mathrm{\%}$

Percentage mass of ${\text{NaHCO}}_{\text{3}}=\frac{\text{0.15g}}{\text{0.2g}+\text{0.15g}}\times 100\mathrm{\%}$

$=42.86\%$