Q. 9. 110 - An Introduction to General, Organic, and Biological Chemistry

Question

What is the initial volume, in milliliters, needed to prepare each of the following diluted solutions? (9.5)

a. $250 mL$of $5.0\% \left(m/v\right)$glucose from $20. \% \left(m/v\right)$ glucose

b. $45.0 mL$ of $1.0\% \left(m/v\right) Ca{\mathrm{CI}}_2$ from $5.0\% \left(m/v\right) {\mathrm{CaCI}}_2$

c. $100. mL$ of $6.00 M{H}_{2}S{O}_4$ from $18.0 M H_{2}S{O}_4$

Step-by-Step Solution

Answer

Part a. $250 mL$ of $5.0\% \left(m/v\right)$ glucose from $20. \% \left(m/v\right)$glucose$=62.5 mL$

Part b. $45.0 mL$ of $1.0\% \left(m/v\right)$${\mathrm{CaCI}}_2$ from $5.0\% \left(m/v\right) {\mathrm{CaCI}}_2$$=9 mL$

Part c. $100. mL$ of $6.00 M H_{2}S{O}_4$ from $18.0 M H_{2}S{O}_4$$= 33 mL$

Step 1: Introduction:

To make several of the preceding responses, they simply dilute the answers within the focus and microliters.

Step 2: Given information :(Part a)

To prepare each of the following solutions, they needed dilute solutions in the initial volume and millilitres.

a. $250 mL$of $5.0\% \left(m/v\right)$ glucose from $20.\% \left(m/v\right)$ glucose

b. $45.0 mL$ of $1.0\% \left(m/v\right)$ ${\mathrm{CaCI}}_2$ from $5.0\% \left(m/v\right) {\mathrm{CaCI}}_2$

c. $100 mL$ of $6.00 M H_{2}S{O}_4$ from $18.0 M H_{2}S{O}_4$

Step 3: According to the dilution expression:

According to the dilution expression:

${\mathrm{C}}_1\times {\mathrm{V}}_1={\mathrm{C}}_2\times {\mathrm{V}}_2$

Here,

${\mathrm{C}}_1$= concentration of the concentrated solution

$V_1$= volume of the concentrated

${\mathrm{C}}_2$ = concentration of the diluted solution

$V_2$ = volume of the diluted solution

Step 5: Part (a) To calculate the glucose solution:

According to the problem,

${\mathrm{C}}_2 = 5.0\% \left(\mathrm{m}/\mathrm{v}\right)$

${\mathrm{V}}_2 = 250 \mathrm{mL}$

${\mathrm{C}}_1 = 20\% \left(\mathrm{m}/\mathrm{v}\right)$

${\mathrm{V}}_1 = ?$

Rearrange the dilution expression to solve for the unknown quantity ${\mathrm{V}}_1$.

$\begin{array}{r}\begin{array}{r}{V}_1=\frac{C_2\times V_2}{C_1}\\ \end{array}\end{array}$

$\begin{array}{r}\\ V_1=\frac{5.0\mathrm{\%} (\mathrm{m}/\mathrm{v})\times 250 \mathrm{mL}}{20.0\mathrm{\%} (\mathrm{m}/\mathrm{v})}\end{array}$

$= 62.5 mL$

The required initial volume of glucose solution is $62.5 mL$

Step 5: Part (b) To calculate the C a C I 2 solution:

According to the problem,

${\mathrm{C}}_2 = 1.0\% \left(\mathrm{m}/\mathrm{v}\right)$

${\mathrm{V}}_2 = 45 \mathrm{mL}$

${\mathrm{C}}_1= 5.0\% \left(\mathrm{m}/\mathrm{v}\right)$

${\mathrm{V}}_1 = ?$

Rearrange the dilution expression to solve for the unknown quantity ${\mathrm{V}}_1.$

$\begin{array}{r}{V}_1=\frac{C_2\times V_2}{C_1}\end{array}$

$\begin{array}{r}\\ V_1=\frac{1.0\mathrm{\%} (\mathrm{m}/\mathrm{v})\times 45 \mathrm{mL}}{5.0\mathrm{\%} (\mathrm{m}/\mathrm{v})}\end{array}$

$=9 mL$

The required initial volume of ${\mathrm{CaCI}}_2$ solution is $9 mL$.

Step 6: Part (c) To calculate the H 2 S O 4 solution:

According to the problem, 

${\mathrm{C}}_2 = 6.0 \mathrm{M}$

${\mathrm{V}}_2= 100 \mathrm{mL}$

${\mathrm{C}}_1= 18.0 \mathrm{M}$

${\mathrm{V}}_1=?$

Rearrange the dilution expression to solve for the unknown quantity ${\mathrm{V}}_1.$

$\begin{array}{r}{V}_1=\frac{C_2\times V_2}{C_1}\\ \end{array}$

$\begin{array}{r}\\ V_1=\frac{6.0 M\times 1000 \mathrm{mL}}{18.0 M}\end{array}$

$=33 mL$

The required initial volume of $H_{2}S{O}_4$ solution is $33 mL.$