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

Hint: 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.