# What is the mass of NH_4Cl that must dissolve in 200 grams of water at 50°C to make a saturated solution?

Mar 24, 2016

Approximately $\text{100 g}$.

#### Explanation:

Your tool of choice here will the solubility graph for ammonium chloride, $\text{NH"_4"Cl}$, which looks like this Before reading the solubility graph, make sure that you have a clear understanding of what it is you're looking for here.

A saturated solution is essentially a solution in which the dissolution and the crystallization of the solute are at equilibrium.

Simply put, the rate at which the ions are dissociated into solution will be equal to the rate at which dissolved ions will recrystallize into the solid. This means that you're looking for the mass of ammonium chloride that will allow the solution to have the maximum concentration of dissolved ions at that given temperature.

Now, the solubility graph will allow you to find the solubility of the solute per $\text{100 g}$ of water at various temperatures. A saturated ammonium chloride solution will correspond to the actual curve of the graph.

At ${50}^{\circ} \text{C}$, ammonium chloride has a solubility of approximately $\text{50 g}$ per $\text{100 g}$ of water.

This means that dissolving $\text{50 g}$ of ammonium chloride in $\text{100 g}$ of water will result in the formation of a saturated solution only at ${50}^{\circ} \text{C}$.

Use this value as a conversion factor to determine how much ammonium chloride can be dissolved in $\text{200 g}$ of water at ${50}^{\circ} \text{C}$

$200 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{g water"))) * overbrace(("50 g NH"_4"Cl")/(100color(red)(cancel(color(black)("g water")))))^(color(purple)("solubility at 50"^@"C")) = color(green)(|bar(ul(color(white)(a/a)"100 g NH"_4"Cl} \textcolor{w h i t e}{\frac{a}{a}} |}}}$