Chapter 17, Problem 47A

Interpretation Introduction

Interpretation:

The molar concentration of manganese in the cube is to be calculated

Concept introduction:

The molar concentration is ratio of number of moles of solute dissolved per unit volume of the solution.

$\text{M=}\frac{\text{n}}{\text{V}}$

Where, n = Number of moles of solute

V = Volume of the solution

Answer to Problem 47A

The molar concentration of manganese cube is $\text{1}{\text{.35×10}}^{\text{2}}\text{mol/L}$.

Explanation of Solution

Given information is: edge of the cube = $\text{5}\text{.25cm}$

Mass of the manganese cube = $\text{1076}\text{.6g}$

Volume of the cube,

$\begin{array}{l}\text{V=}{\left(\text{5}\text{.25}\right)}^{\text{3}}\\ \text{=144}{\text{.70×10}}^{\text{-3}}\end{array}$

And, number of moles,

$\begin{array}{l}\text{n=}\frac{\text{1076}\text{.6}}{\text{54}\text{.938}}\\ \text{=19}\text{.6}\end{array}$

The molar concentration is ratio of number of moles of solute dissolved per unit volume of the solution.

$\text{M=}\frac{\text{n}}{\text{V}}$

Where, n = Number of moles of solute

V = Volume of the solution

$\begin{array}{l}\text{M=}\frac{\text{19}\text{.6}}{\text{144}{\text{.7×10}}^{\text{-3}}}\\ \text{=0}{\text{.135×10}}^{\text{3}}\\ \text{=1}{\text{.35×10}}^{\text{2}}\text{mol/L}\end{array}$

The molar concentration of manganese cube is $\text{1}{\text{.35×10}}^{\text{2}}\text{mol/L}$.

Conclusion

The molar concentration of manganese cube is $\text{1}{\text{.35×10}}^{\text{2}}\text{mol/L}$.