Q3.95P - Chemistry: Molecular Nature Of Matter And Change

Question

Are the following instructions for diluting a 10.0 M solution to a 1.00 M solution correct: “Take 100.0 mL of the 10.0 M solution and add 900.0 mL water”? Explain.

Step-by-Step Solution

Answer

Answer

The given instructions are correct for diluting the given sample. So, adding 900 mL of water to 10.0 M (100 mL) solution will change the molarity to 1M.

Step 1: Relation between molarity of a dilute and concentrated solution

For this process following equation can be used,

${\mathit{M}}_{\mathbf{d}\mathbf{i}\mathbf{l}}\mathbf{\times }{\mathit{V}}_{\mathbf{d}\mathbf{i}\mathbf{l}}\mathbf{=}{\mathit{M}}_{\mathbf{c}\mathbf{o}\mathbf{n}\mathbf{c}}\mathbf{\times }{\mathit{V}}_{\mathbf{c}\mathbf{o}\mathbf{n}\mathbf{c}\mathbf{.}}$

${\mathit{M}}_{\mathbf{dil}}$= molarity of dilute solution,

${\mathit{V}}_{\mathbf{dil}}$= volume of the dilute solution,

${\mathit{M}}_{\mathbf{conc}}$= molarity of concentrated solution and

${\mathit{V}}_{\mathbf{conc}}$= volume of the concentrated solution.

Step 2: Calculation of Volume of a dilute solution

From the equation given above, we can say that 

${\mathit{V}}_{\left(dil\right)}\mathbf{=}\frac{{\mathbf{M}}_{\left(conc\right)}\mathbf{\times }{\mathbf{V}}_{\left(conc\right)}}{{\mathbf{M}}_{\left(dil\right)}}\mathbf{=}\frac{\mathbf{10}\mathbf{ }\mathbf{M}\mathbf{\times }\mathbf{100}\mathbf{ }\mathbf{m}\mathbf{L}}{\mathbf{1}\mathbf{ }\mathbf{M}}\mathbf{=}\mathbf{1000}\mathbf{ }\mathit{m}\mathit{L}$

Thus, the volume of diluted solution must be 1000 mL so 900 needs to be added to the concentrated solution. So, the given instructions are correct for diluting the given sample.