Question

When a 2.558g sample of washing soda (Na2CO3 x XH20) is heated, all the water of hydration is lost, leaving 0.948g of Na2CO3. What is the value of X?

Answer 1

When a 2.558g sample of washing soda (Na₂CO₃ × XH₂O) is heated, all the water of hydration is lost, leaving 0.948g of Na₂CO₃. What is the value of X?

**Solution:** The process of dehydration can be described with the following equation:

$$\mathrm{Na_2CO_3} \times \mathrm{XH_2O} = \mathrm{Na_2CO_3} + \mathrm{XH_2O}$$

The quantity of moles of $\mathrm{Na_2CO_3}$ left: $\nu(\mathrm{Na_2CO_3}) = \frac{m(\mathrm{Na_2CO_3})}{M(\mathrm{Na_2CO_3})} = \frac{0.984g}{106g/mol} = 0.0093mol$

The quantity of moles of $\mathrm{Na_2CO_3}$ is equal to the quantity of moles of the washing soda $\mathrm{Na_2CO_3} \times \mathrm{XH_2O}$ (from the reaction equation), $\nu(\mathrm{Na_2CO_3} \times \mathrm{XH_2O}) = \nu(\mathrm{Na_2CO_3}) = 0.0093\mathrm{mol}$. In order to solve the formula of the washing soda, the molar mass of it must be calculated:

$$\nu(\mathrm{Na_2CO_3} \times \mathrm{XH_2O}) = \frac{m(\mathrm{Na_2CO_3} \times \mathrm{XH_2O})}{M(\mathrm{Na_2CO_3} \times \mathrm{XH_2O})} : M(\mathrm{Na_2CO_3} \times \mathrm{XH_2O}) = \frac{m(\mathrm{Na_2CO_3} \times \mathrm{XH_2O})}{\nu(\mathrm{Na_2CO_3} \times \mathrm{XH_2O})} = \frac{2.558g}{0.0093mol} = 275g/mol$$

Molar mass of the substance is the sum of molar masses of its components (atoms):

$$M(\mathrm{Na_2CO_3} \times \mathrm{XH_2O}) = M(\mathrm{Na_2CO_3}) + X * M(\mathrm{H_2O});$$ $$275g/mol = 106g/mol + (X * 18)g/mol$$ $$169g/mol = (X * 18)g/mol$$ $$X = \frac{169g/mol}{18g/mol} = 9.4$$

**Answer:** $X = 9.4$