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# Solubility Curve

The solubility of a solid in a given solvent is defined as the number of grams of the solute required to saturate 100g of the solvent at a particular temperature. The solubility of given substance at a given temperature can be determined from its solubility curve. Solubility curve can be used to determine the amount of substance deposited when the solution is cooled. Solubilities of different substances at a particular temperature can be determined.

When any solid is in contact with its solution for sufficient time, then the solid will dissolve if the solution is not saturated or the solid will grow at the expense of the solution if the solution is supersaturated. In any case the solubility cure represents equilibrium conditions.

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## Solubility Curve Definition

The variation in the solubility of any given substance with change of temperature is shown by solubility curve. The curve line drawn on a graph showing the relationship between temperature and solubility of the substance at different temperature is called a solubility curve.

A graphical relationship between the solubility and temperature is termed as the solubility curve. The solubility curve plots the changes of the solubility of a solid at different temperatures in a solvent. On a graph, the variations in temperature are plotted on X-axis and the solubility is plotted on the Y-axis. Temperature plays an important role in solubility because the solubility of a substance is different at different temperatures.

## How to Read a Solubility Curve?

Consider the solubility curve of different salts in water.

The solubility curves have no general shape or slope. Solubility curve of potassium chlorate, sodium chloride are continuous solubility curves as they show no sharp breaks anywhere. Sometimes the solubility curve exhibits sudden changes of direction and these curves are therefore referred to as a discontinuous solubility curve for example FeSO4 and Na2SO4 etc.

Usually increase in the temperature of the solution increases the solubility of the solute when no true compounds are formed between the solute and solvent. In case of hydrated salt the solubility increases with increase in temperature over a certain temperature range and then decreases. For some specific substances, the solubility decreases with increase in temperature and in such cases their solubility cures are called as inverted solubility curves.

## Importance of Solubility Curve

Solubility curve can be used to determine the amount of substance deposited when the solution is cooled. Solubilities of different substances at a particular temperature can be determined. The importance of solubility curve is listed below.
1. The solubility of a substance at a particular temperature can be determined.
2. The solubility of a given substance at any temperature can be determined.
3. The solubility curve helps us to predict which substance will crystallize out first from a solution containing two or more solutes.
4. The solubility curve helps us to compare the solubilities of different substances at the same temperature.
5. It brings the change in the composition of a solute substance.
6. It gives a clear idea that solubility of substance changes with the temperature.

## How to Draw a Solubility Curve?

The solubility of a solid in a given solvent is defined as the number of grams of the solute required to saturate 100g of the solvent at a particular temperature. Consider the example of the solubility of two compounds KNO3 and CuSO4.5H2O in different temperature. The temperature which was controlled is collected in horizontal axis. The solubility in grams per 100 grams water was measured quantity produced the data in vertical axis.

The data can be extracted from the graph. To find the solubility of KNO3 at 60oC draw the dashed line up from 60oC. The solubility is given by the point at which that line intersects the KNO3 graph line. Draw a horizontal line from that intersection to the vertical axis and read off the solubility of KNO3. Like this in many chemical experiments one of the measured quantities is dependent on another. If one is changed, the another automatically changes. In such cases, the graph represented in two dimensional, which is shown in a continuous was how one quantity depends on another.

## Solubility Curve Problems

Some of the solved problems based on solubility curve are given below:

Question 1: A solution in equilibrium with a precipitate of AgCl was found, on analysis, it contains 1.0 $\times$ 10-4 mol of Ag+/L and 1.7 $\times$ 10-6 mol of Cl-/L. Calculate the solubility product of AgCl.
Solution:

The solubility product is by definition the product of the concentrations of the ions in equilibrium with a precipitate of a sparingly soluble substance.

For AgCl

Ksp = [Ag+][Cl-]

= (1.0 $\times$ 10-4) $\times$ (1.7 $\times$ 10-6)

= 1.7 $\times$ 10-10

Question 2: A solution in equilibrium with a precipitate of Ag2S was found on analysis to contain 6.3 $\times$ 10-18mol of S2/L and 1.26 $\times$ 10-7mol of Ag+/L. Calculate the solubility product of Ag2S.
Solution:

Ksp (Ag2S) = [Ag+]2 $\times$ [S2-]

= (1.26 $\times$ 10-17)2 $\times$ (6.3 $\times$ 10-18)

= 1.0 $\times$ 10-51
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