Q93P - Chemistry: Molecular Nature Of Matter And Change

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?

Step-by-Step Solution

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 1: Determination of Symbols

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

Step 2: 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 

 

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

Step 3: Calculation of mass and moles of CaCI 2

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:

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