Q13.73 P - Chemistry: Molecular Nature Of Matter And Change

Question

What are the mole fraction and the mass percent of a solution made by dissolving 0.30 g of KI in 0.400 L of water (d = 1.00 g/mL)?

Step-by-Step Solution

Answer

The mole fraction of KI is 0.000091 and the mass percent of solution formed from KI and water is 0.075%.

Step 1: Concentration of the Solution

Solution can be formed from the dissolution of the solute in the solvent. The solute decides the nature of the solution.

Molality can be defined as the ratio of the mass of the solute to the mass of the solution present in kilogram measure.

$\mathbf{Molality}\mathbf{=}\frac{\mathbf{Number} \mathbf{of} \mathbf{Moles}}{\mathbf{Mass} \mathbf{of} \mathbf{the} \mathbf{Solution} \mathbf{(} \mathbf{in} \mathbf{kilogram} \mathbf{)}}$

Number of moles can be defined as the ratio of the mass of the atom/molecule and molar mass of the atom/molecule.

$\mathbf{Number} \mathbf{of} \mathbf{Moles}\mathbf{=}\frac{\mathbf{Mass}}{\mathbf{Molar} \mathbf{Mass}}$

Mole Fraction can be defined as the ratio of the number of moles of the solute to the number of moles of solvent and number of solute.

$\mathbf{Mole} \mathbf{Fraction}\mathbf{=}\frac{\mathbf{Number} \mathbf{of} \mathbf{Moles} \mathbf{of} \mathbf{One} \mathbf{Component}}{\mathbf{Number} \mathbf{of} \mathbf{Moles} \mathbf{of} \mathbf{the} \mathbf{Solvent}\mathbf{+}\mathbf{Number} \mathbf{of} \mathbf{Moles} \mathbf{of} \mathbf{Solute}}$

Parts by mass: It can be defined as the percentage of the ratio of the mass of solute to the total mass of the solution.

$\mathbf{Mass}\%\mathbf{=}\frac{\mathbf{Mass} \mathbf{of} \mathbf{Solute}}{\mathbf{Mass} \mathbf{of} \mathbf{the} \mathbf{Solution}}\mathbf{\times }\mathbf{100}$

Density can be defined as the ratio of the mass of the matter to the volume of the matter.

$\mathbf{Density}\mathbf{=}\frac{\mathbf{Mass}}{\mathbf{Volume}}$

Step 2: Expression to calculate the Concentration

Volume of Water $\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{400}\mathbf{L}\mathbf{=}\mathbf{400}\mathbf{mL}$

Density of the Water $\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{g}\mathbf{/}\mathbf{mL}$

$$\begin{gathered} \mathbf{Density}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{Water}\mathbf{=}\frac{\mathbf{Mass}}{\mathbf{Volume}} \\ \mathbf{1}\mathbf{.}\mathbf{0}\mathbf{g}\mathbf{/}\mathbf{mL}\mathbf{=}\frac{\mathbf{Mass}}{\mathbf{400}\mathbf{mL}} \\ \mathbf{Mass}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{g}\mathbf{/}\mathbf{mL}\mathbf{\times }\mathbf{400}\mathbf{mL} \\ \mathbf{Mass}\mathbf{=}\mathbf{400}\mathbf{g} \end{gathered}$$

Mass of water $\mathbf{=}\mathbf{400}\mathbf{g}$

$$\begin{gathered} \mathbf{Number}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{Moles}\mathbf{=}\frac{\mathbf{Mass}}{\mathbf{Molar}\mathbf{ }\mathbf{Mass}} \\ \mathbf{NumberofMoles}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{Water}\mathbf{=}\frac{\mathbf{400}\mathbf{g}}{\mathbf{18}\mathbf{g}\mathbf{/}\mathbf{mol}} \\ \mathbf{NumberofMoles}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{Water}\mathbf{=}\mathbf{22}\mathbf{ }\mathbf{mol} \end{gathered}$$

Mass of KI  $\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{30}\mathbf{g}$

Molar Mass of KI  $\mathbf{=}\mathbf{166}\mathbf{g}\mathbf{/}\mathbf{mole}$

$$\begin{gathered} \mathbf{Number} \mathbf{of} \mathbf{Moles}\mathbf{=}\frac{\mathbf{Mass}}{\mathbf{Molar} \mathbf{Mass}} \\ \mathbf{NumberofMoles} \mathbf{of} \mathbf{KI}\mathbf{=}\frac{\mathbf{0}\mathbf{.}\mathbf{30}\mathbf{g}}{\mathbf{166}\mathbf{g}\mathbf{/}\mathbf{mol}} \\ \mathbf{NumberofMoles} \mathbf{of} \mathbf{KI}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{002}\mathbf{mol} \end{gathered}$$

Number of moles of water  $\mathbf{=}\mathbf{22}\mathbf{mole}$

Number of KI  ${\mathbf{n}}_{\mathbf{KI}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{002}\mathbf{mol}$

$$\begin{gathered} \mathbf{Mole}\mathbf{ }\mathbf{Fraction}\mathbf{=}\frac{\mathbf{Number}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{Moles}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{One}\mathbf{ }\mathbf{Component}}{\mathbf{Number}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{Moles}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{the}\mathbf{ }\mathbf{Solvent}\mathbf{+}\mathbf{Number}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{Moles}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{Solute}} \\ \mathbf{Mole}\mathbf{ }\mathbf{Fraction}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{Kl}\mathbf{=}\frac{\mathbf{0}\mathbf{.}\mathbf{002}}{\mathbf{22}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{002}} \\ \mathbf{Mole}\mathbf{ }\mathbf{Fraction}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{Kl}\mathbf{=}\frac{\mathbf{0}\mathbf{.}\mathbf{002}}{\mathbf{22}\mathbf{.}\mathbf{002}} \\ \mathbf{Mole}\mathbf{ }\mathbf{Fraction}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{Kl}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{000091} \end{gathered}$$

Mass of solute, KI  $\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{30}\mathbf{g}$

Mass of solvent, water   $\mathbf{=}\mathbf{400}\mathbf{g}$

$$\begin{gathered} \mathbf{Mass}\%\mathbf{=}\frac{\mathbf{Mass} \mathbf{of} \mathbf{Solute}}{\mathbf{Mass} \mathbf{of} \mathbf{the} \mathbf{Solution}}\mathbf{\times }\mathbf{100} \\ \mathbf{=}\frac{\mathbf{0}\mathbf{.}\mathbf{30}\mathbf{g}}{\mathbf{400}\mathbf{g}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{30}\mathbf{g}}\mathbf{\times }\mathbf{100} \\ \mathbf{=}\frac{\mathbf{0}\mathbf{.}\mathbf{30}\mathbf{g}}{\mathbf{400}\mathbf{.}\mathbf{30}\mathbf{g}}\mathbf{\times }\mathbf{100} \\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{075}\mathbf{\%} \end{gathered}$$