Chapter 10, Problem 180A

Determine the mass percent of anhydrous sodium carbonate $\left({\text{Na}}_{\text{2}}{\text{CO}}_{\text{3}}\right)$ and water in sodium carbonate decahydrate $\left({\text{Na}}_{\text{2}}{\text{CO}}_{\text{3}}\cdot 1{\text{0H}}_{\text{2}}\text{O}\right)$ .

Interpretation Introduction

Interpretation:

Mass percentage of sodium carbonate and water must be calculated in sodium carbonate decahydrate.

Concept introduction:

1 molecule of sodium carbonate decahydrate contains 1 formula unit of sodium carbonate and 10 molecules of water.

Mass % of a species in a compound $\text{=}\frac{\text{molar mass of the species}}{\text{Molar mass of the compound}}\times 100\%$

Answer to Problem 180A

Percentage mass of Na₂CO₃ is 37.06% and percentage mass of water is 62.94%.

Explanation of Solution

Molar mass of Na₂CO₃.10 H₂O is 286 g/mol.

Molar mass of Na₂CO₃ is 106 g/mol.

Molar mass of H₂O is 18 g/mol.

Now, from total mass of hydrated salt, the mass percent of sodium carbonate and water can be calculated as follows:

Mass % of Na₂CO₃$\text{=}\frac{\text{106×100\%}}{\text{286}}\text{=}\frac{\text{10600}}{\text{286}}\text{\%=37}\text{.06\%}$

Mass % of H₂O $\text{=}\frac{\text{10×18×100\%}}{\text{286}}\text{=}\frac{\text{18000}}{\text{286}}\text{\%=62}\text{.94\%}$

Conclusion

Thus, mass percentage of Na₂CO₃ and H₂O are 37.06% and 62.94% respectively.