Chapter 16, Problem 39E

Interpretation Introduction

Interpretation:

The molarity of solutions on dissolving $\text{18}\text{.0}\text{g}$ of anhydrous nickel $\left(\text{II}\right)$ chloride and $\text{30}\text{.0}\text{g}$ of nickel $\left(\text{II}\right)$ chloride hexahydrate separately in $90.0\text{mL}$ water is to be calculated. The solution with the higher molar concentration is to be identified.

Concept Introduction:

Molarity is defined as the number of moles present in one liter of solution. General expression is shown below.

$\text{Molarity}=\frac{\text{Moles}\text{of}\text{solute}}{\text{Volume}\text{of}\text{solution}}$

Measuring unit of molarity is $\text{mol}/\text{L}$ or $\text{molar}\left(\text{M}\right)$.

Answer to Problem 39E

The molarity of $\text{18}\text{.0}\text{g}$ of anhydrous nickel $\left(\text{II}\right)$ chloride and $\text{30}\text{.0}\text{g}$ of nickel $\left(\text{II}\right)$ chloride dissolved separately in $90.0\text{mL}$ water is $1.54\text{M}{\text{NiCl}}_{\text{2}}$ and $1.4\text{M}{\text{NiCl}}_{\text{2}}{\text{.6H}}_{\text{2}}\text{O}$ respectively. The molar concentration of anhydrous nickel $\left(\text{II}\right)$ chloride is higher than that of nickel $\left(\text{II}\right)$ chloride hexahydrate.

Explanation of Solution

The molarity of solution when $\text{18}\text{.0}\text{g}$ of anhydrous nickel $\left(\text{II}\right)$ chloride is dissolved in $90.0\text{mL}$ water is calculated by the formula given below.

$\text{Molarity}=\frac{\text{Moles}\text{of}\text{solute}}{\text{Volume}\text{of}\text{solution}}$ … (1)

The molar mass of anhydrous nickel $\left(\text{II}\right)$ chloride is $129.59\text{g}/\text{mol}$.

Number of moles of $\text{18}\text{.0}\text{g}$ of anhydrous nickel $\left(\text{II}\right)$ chloride is calculated as shown below.

$\begin{array}{rll}\text{Moles}\text{of}{\text{NiCl}}_{\text{2}}& =& \frac{\text{Given}\text{mass}\text{of}{\text{NiCl}}_{\text{2}}}{\text{Molar}\text{mass}\text{of}{\text{NiCl}}_{\text{2}}}\\ & =& 18.0\text{g}{\text{NiCl}}_{\text{2}}\times \frac{\text{1}\text{mol}{\text{NiCl}}_{\text{2}}}{129.59\text{g}{\text{NiCl}}_{\text{2}}}\\ & =& \text{0}\text{.139}\text{mol}{\text{NiCl}}_{\text{2}}\end{array}$

The molarity of anhydrous nickel $\left(\text{II}\right)$ chloride is calculated using equation (1) as shown below.

$\begin{array}{rll}\text{Molarity}\text{of}{\text{NiCl}}_{\text{2}}& =& \frac{\text{0}\text{.138}\text{mol}{\text{NiCl}}_{\text{2}}}{\text{90}\text{.0}\text{mL}}\times \frac{\text{1000}\text{mL}}{\text{1}\text{L}}\\ & =& 1.54\text{M}{\text{NiCl}}_{\text{2}}\end{array}$

The molar mass of anhydrous nickel $\left(\text{II}\right)$ chloride hexahydrate is $237.69\text{g}/\text{mol}$.

Number of moles of $\text{30}\text{.0}\text{g}$ of nickel $\left(\text{II}\right)$ chloride hexahydrate in $90.0\text{mL}$ water is calculated as shown below.

$\begin{array}{rll}\text{Moles}\text{of}{\text{NiCl}}_{\text{2}}{\text{.6H}}_{\text{2}}\text{O}& =& \frac{\text{Given}\text{mass}\text{of}{\text{NiCl}}_{\text{2}}{\text{.6H}}_{\text{2}}\text{O}}{\text{Molar}\text{mass}\text{of}{\text{NiCl}}_{\text{2}}{\text{.6H}}_{\text{2}}\text{O}}\\ & =& 30.0\text{g}{\text{NiCl}}_{\text{2}}{\text{.6H}}_{\text{2}}\text{O}\times \frac{\text{1}\text{mol}{\text{NiCl}}_{\text{2}}{\text{.6H}}_{\text{2}}\text{O}}{237.69\text{g}{\text{NiCl}}_{\text{2}}{\text{.6H}}_{\text{2}}\text{O}}\\ & =& \text{0}\text{.126}\text{mol}{\text{NiCl}}_{\text{2}}{\text{.6H}}_{\text{2}}\text{O}\end{array}$

The molarity of anhydrous nickel $\left(\text{II}\right)$ chloride hexahydrate is calculated using equation (1) as shown below.

$\begin{array}{rll}\text{Molarity}\text{of}{\text{NiCl}}_{\text{2}}{\text{.6H}}_{\text{2}}\text{O}& =& \frac{\text{0}\text{.126}\text{mol}{\text{NiCl}}_{\text{2}}{\text{.6H}}_{\text{2}}\text{O}}{\text{90}\text{.0}\text{mL}}\times \frac{\text{1000}\text{mL}}{\text{1}\text{L}}\\ & =& 1.4\text{M}{\text{NiCl}}_{\text{2}}{\text{.6H}}_{\text{2}}\text{O}\end{array}$

Therefore, the molar concentration of anhydrous nickel $\left(\text{II}\right)$ chloride is higher than that of nickel $\left(\text{II}\right)$ chloride hexahydrate.

Conclusion

The molarity of solutions on dissolving $\text{18}\text{.0}\text{g}$ of anhydrous nickel $\left(\text{II}\right)$ chloride and $\text{30}\text{.0}\text{g}$ of nickel $\left(\text{II}\right)$ chloride hexahydrate separately in $90.0\text{mL}$ water is calculated as $1.54\text{M}{\text{NiCl}}_{\text{2}}$ and $1.4\text{M}{\text{NiCl}}_{\text{2}}{\text{.6H}}_{\text{2}}\text{O}$ respectively. The molar concentration of anhydrous nickel $\left(\text{II}\right)$ chloride is found to be higher than that of nickel $\left(\text{II}\right)$ chloride hexahydrate.