Chapter 10, Problem 187A

Borax Hydrated sodiumtetraborate $\left({\text{Na}}_{\text{2}}{\text{B}}_{\text{4}}{\text{O}}_{\text{7}}\text{•}x{\text{H}}_{\text{2}}\text{O}\right)$ is commonly called borax. Chemical analysis indicates that this hydrate is 52.8% sodium tetraborate and 47.2% water. Determine the formula and name the hydrate.

Interpretation Introduction

Interpretation:

Formula and name of the hydrate compound needs to be determined which is 52.8 % Na₂B₄O₇ and 47.2 % H₂O.

Concept introduction:

Percentage mass of an entity in a compound can be calculated as follows:

$\%m\text{=}\frac{\text{Molar mass of the entity}}{\text{Molar mass of the compound}}\text{×100}\%$

Answer to Problem 187A

Formula of the hydrate is Na₂B₄O₇.10H₂O. Name of the hydrate is sodium tetraborate decahydrate.

Explanation of Solution

Molar mass of Na₂B₄O₇ is 202 g/mol.

Molar mass of H₂O is 18 g/mol.

52.8% Na₂B₄O₇means 52.8 g Na₂B₄O₇ combines with 47.2 g H₂O.

The number of moles of Na₂B₄O₇ and H₂O can be calculated as follows:

Mole of Na₂B₄O₇$=\frac{52.8\text{ g}}{202\text{ g/mol}}=0.261\text{ mol}$

Mole of H₂O $=\frac{47.2\text{ g}}{18\text{ g/mol}}=2.62\text{ mol}$

Mole ratio of Na₂B₄O₇: H2O $=0.261:2.62=1:10.04\approx 1:10.$

So the formula is Na₂B₄O₇.10H₂O.

Name of the hydrate is sodium tetraborate decahydrate.

Conclusion

Formula of the given hydrate is Na₂B₄O₇.10H₂O and it is called sodium tetraborate decahydrate.