Question

What volume $\left( {mL} \right)$ of a concentrated solution of sodium hydroxide $\left( {6.00M} \right)$ solution must be dilute to $200.0{\text{ }}ml$ to make a $0.880M\;$ solution of sodium hydroxide ?

Answer 1

In the above mentioned question, we will find out the concentration of sodium hydroxide diluted in $200.0mL$ to make a $0.880{\text{ }}M$ Solution of sodium hydroxide by using the dilution formula ${M_1}{V_1} = {M_2}{V_2}$ .

Complete step by step answer:
We know the dilution formula $,{\text{ }}{M_1}{V_1}{\text{ }} = {\text{ }}{M_2}{V_2}$
where ${M_1}{\text{ }} = {\text{ }}initial{\text{ }}concentration{\text{ }}of{\text{ }}the{\text{ }}solution$
${M_2}{\text{ }} = {\text{ }}final{\text{ }}concentration{\text{ }}of{\text{ }}the{\text{ }}solution$
${V_2}{\text{ }} = {\text{ }}final{\text{ }}volume{\text{ }}of{\text{ }}the{\text{ }}solution$
$given,{\text{ }}{V_1}{\text{ }} = {\text{ }}to{\text{ }}be{\text{ }}determined$
${M_1}{\text{ }} = {\text{ }}6.00{\text{ }}M$
${V_2}{\text{ }} = 200mL$
${M_2}{\text{ }} = {\text{ }}0.880M$
from the formula we can write,
$V1{\text{ }} = {\text{ }}\left( {{M_2}{V_2}} \right)/{\text{ }}{M_2}{\text{ }} = {\text{ }}\left( {200 \times {\text{ }}0.880} \right){\text{ }}/{\text{ }}6{\text{ }} = {\text{ }}29.33{\text{ }}mL$
Therefore , the initial volume of $NaOH$ Solution required is $29.33mL$ .

Note:
The dilution equation determines the time required to reduce a known vapour concentration existing in a closed space to a lower vapor concentration. The equation can only be applied when the purged volume of vapor or gas is replaced with "clean" air or gas.