Chapter U4, Problem 18STP

Interpretation Introduction

Interpretation:

The mass of sodium chloride produced from the production of 5.0 g calcium oxalate needs to be calculated.

Concept introduction:

The mathematical relationship between number of moles, mass of substance and molar mass is:

$\text{number of moles = }\frac{\text{mass of the substance}}{\text{Molar mass of the substance}}$ - (1)

Answer to Problem 18STP

The correct option is (b) $4.6\text{ g NaCl}$.

Explanation of Solution

Given:

${\text{CaCl}}_{\text{2}}{\text{(aq) + Na}}_2{\text{C}}_{\text{2}}{\text{O}}_{\text{4}}\text{(aq)}\to {\text{2NaCl(aq) + CaC}}_{\text{2}}{\text{O}}_{\text{4}}\text{(aq)}$

Calculating the number of moles of calcium oxalate present in 5.0 g of calcium oxalate using formula:

$\text{number of moles = }\frac{\text{mass of the substance}}{\text{Molar mass of the substance}}$

The molar mass of calcium oxalate is $\text{128}\text{.097 g/mol}$.

Substituting the values:

$\begin{array}{l}\text{number of moles = }\frac{5.0\text{ g}}{\text{128}\text{.097 g/mol}}\\ \text{number of moles = }0.039\text{ mol}\end{array}$

From the given balanced reaction, it can be observed that the mole ratio between sodium chloride, $\text{NaCl}$ and calcium oxalate, ${\text{CaC}}_{\text{2}}{\text{O}}_{\text{4}}$ is $\text{2:1}$ that is two moles of sodium chloride are produced with every one mole of calcium oxalate. So, the moles of $\text{NaCl}$ produced from $0.039\text{ mol}$ of ${\text{CaC}}_{\text{2}}{\text{O}}_{\text{4}}$ is:

$0.039\text{ mol }\times 2\text{ = 0}\text{.078 mol}$

Now, the mass of sodium chloride is obtained by rearranging the equation (1) as:

$\text{mass of the substance = number of moles}\times \text{Molar mass of the substance}$

The molar mass of sodium chloride is $\text{58}\text{.44 g/mol}$.

Substituting the values:

$\begin{array}{l}\text{mass of NaCl = 0}\text{.078 mol}\times \text{58}\text{.44 g/mol}\\ \text{mass of NaCl = }4.56\text{ g }\simeq 4.6\text{ g}\end{array}$

Hence, the correct option is (b) $4.6\text{ g NaCl}$.

Conclusion

The mass of sodium chloride produced from the production of 5.0 g calcium oxalate is $4.6\text{ g}$.