Question

A mathematical equation useful for dilution calculations is ${\mathbf{M}}_{\mathbf{dil}}\mathbf{}\mathbf{\times }{\mathbf{V}}_{\mathbf{dil}}\mathbf{=}{\mathbf{M}}_{\mathbf{conc}}\mathbf{\times }{\mathbf{V}}_{\mathbf{conc}\mathbf{.}}$

(a) What does each symbol mean, and why does the equation work?

(b) Given the volume and molarity of a CaCl₂ solution, how do you determine the number of moles and the mass of solute?

Short answer

$$\begin{gathered} \left(\mathrm{a}\right)\mathrm{The}\mathrm{terms}\mathrm{used}\mathrm{are} \\ {\mathbf{M}}_{\mathbf{dil}\mathbf{}}=\mathrm{molarity}\mathrm{of}\mathrm{dilute}\mathrm{solution}, \\ {\mathbf{V}}_{\mathbf{dil}\mathbf{}}\mathrm{I}=\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{dilute}\mathrm{solution}, \\ {\mathbf{M}}_{\mathbf{conc}\mathbf{}}=\mathrm{molarity}\mathrm{of}\mathrm{concentrated}\mathrm{solution}\mathrm{and} \\ {\mathbf{V}}_{\mathbf{conc}\mathbf{}}=\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{concentrated}\mathrm{solution}. \\ \left(\mathrm{b}\right)\mathrm{Moles}\mathrm{and}\mathrm{mass}\mathrm{can}\mathrm{be}\mathrm{calculated}\mathrm{using}\mathrm{the}\mathrm{formula}, \\ \mathbf{}\mathbf{Moles}\mathbf{}\mathbf{of}\mathbf{}\mathbf{solute}\mathbf{}\mathbf{=}\mathbf{Molarity}\mathbf{\times }\mathbf{Volume}\mathbf{}\mathbf{of}\mathbf{}\mathbf{solution}\mathbf{}\mathbf{\left(}\mathbf{L}\mathbf{\right)}\mathbf{}\mathbf{} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{Mass}\mathbf{=}\mathbf{Moles}\mathbf{\times }\mathbf{111}\mathbf{g} \end{gathered}$$

Step-by-step solution

Determination of Symbols

$$\begin{gathered} \mathrm{Here}\mathrm{for}\mathrm{the}\mathrm{given}\mathrm{equation}, \\ {\mathbf{M}}_{\mathbf{dil}}\mathbf{\times }{\mathbf{V}}_{\mathbf{dil}}\mathbf{=}{\mathbf{M}}_{\mathbf{conc}}\mathbf{\times }{\mathbf{V}}_{\mathbf{conc}\mathbf{.}} \\ {\mathbf{M}}_{\mathbf{dil}}=\mathrm{molarity}\mathrm{of}\mathrm{dilute}\mathrm{solution}, \\ {\mathbf{V}}_{\mathbf{dil}\mathbf{}}=\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{dilute}\mathrm{solution}, \\ {\mathbf{M}}_{\mathbf{conc}\mathbf{}}=\mathrm{molarity}\mathrm{of}\mathrm{concentrated}\mathrm{solution}\mathrm{and} \\ {\mathbf{V}}_{\mathbf{conc}}=\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{concentrated}\mathrm{solution}. \end{gathered}$$

Determination of Molarity

Molarity is defined as the number of moles of solute per unit volume of the solution. Formula for molarity is given as

$\mathbf{Molarity}\mathbf{}\mathbf{=}\frac{\mathbf{Moles}\mathbf{}\mathbf{of}\mathbf{}\mathbf{solute}}{\mathbf{Volume}\mathbf{}\mathbf{of}\mathbf{}\mathbf{solution}\mathbf{}\mathbf{\left(}\mathbf{L}\mathbf{\right)}}$

Calculation of mass and moles of CaCI2

If molarity and volume are given moles can be calculated as:

$\mathbf{Moles}\mathbf{}\mathbf{of}\mathbf{}\mathbf{solute}\mathbf{=}\mathbf{Molarity}\mathbf{\times }\mathbf{Volume}\mathbf{}\mathbf{of}\mathbf{}\mathbf{solution}\mathbf{}\mathbf{\left(}\mathbf{L}\mathbf{\right)}$

Mass can be calculated from the moles:

$\mathbf{MAss}\mathbf{=}\mathbf{Moles}\mathbf{\times }\mathbf{Molar}\mathbf{}\mathbf{mass}$

For ${\mathbf{CaCI}}_{\mathbf{2}}$after calculating moles, mass can be calculated as:

$\mathbf{Mass}\mathbf{=}\mathbf{Moles}\mathbf{\times }\mathbf{111}\mathbf{g}(\mathrm{as}\mathrm{molar}\mathrm{mass}\mathrm{of}{\mathbf{CaCI}}_{\mathbf{2}}=111\mathrm{g})$