Question

Question: A student prepares a solution by dissolving $\mathbf{1}\mathbf{.}\mathbf{000}\mathbf{}\mathit{m}\mathit{o}\mathit{l}$of${\mathbf{\text{Na}}}_{\mathbf{2}}{\mathbf{\text{SO}}}_{\mathbf{4}}$in water. She accidentally leaves the container uncovered and comes back the next week to find only a white, solid residue. The mass of the residue isrole="math" localid="1663417226159" $\mathbf{322}\mathbf{.}\mathbf{2}\mathit{g}$. Determine the chemical formula of this residue.

Short answer

The formula of the substance is ${\text{Na}}_2{\text{SO}}_4·\mathbf{10}{\text{H}}_2\text{O}$sodium sulfate decahydrate is the residue.

Step-by-step solution

Given data

The mass of the residue is$322.2g$.

Concept of Crystallization

Crystallization can be defined as the solidification of a liquid substance into a highly structured solid whose atoms or molecules are placed in a well-defined three-dimensional crystal lattice.

Determine the chemical formula of residue

If the salts with water crystallization is prepared by using$1mol$of the non-volatile sodium sulfate, then residue must contain all of it.

The rest of the mass, even in its solid (crystalline) state may be water molecules. This form of the salts is called a hydrate, with the following structure:

${\text{Na}}_2{\text{SO}}_4·n{\text{H}}_2\text{O}$

The molar mass is additive.

Therefore,

$$\begin{gathered} M_{\left({\text{Na}}_2{\text{SO}}_4·n{\text{H}}_2\text{O}\right)}=M_{{\text{Na}}_2{\text{SO}}_4}+n\times M_{{\text{H}}_2\text{O}} \\ 322.2=142.04+n\times 18.02 \\ n=10.00 \end{gathered}$$

The formula of the substance is${\mathbf{Na}}_2{\text{SO}}_4·\mathbf{10}{\text{H}}_2\text{O}$ with the proper name sodium sulfate decahydrate, also Glauber's salt.