Question

The solubility of sugar is \(110 \mathrm{~g} / 100 \mathrm{~g}\) water at \(30^{\circ} \mathrm{C} .\) If a solution contains \(95 \mathrm{~g}\) of sugar in \(25 \mathrm{~g}\) of water at \(30{ }^{\circ} \mathrm{C},\) is the solution saturated, unsaturated, or supersaturated?

Short answer

The solution is supersaturated because it contains more sugar than the solubility allows at 30°C.

Step-by-step solution

Understand Solubility

The solubility of a substance indicates how much of that substance can dissolve in a solvent at a given temperature. Here, sugar's solubility is given as 110 g per 100 g of water at 30°C.

Calculate Relative Proportion

We need to understand how much sugar should be dissolved in 25 g of water when the solubility is 110 g in 100 g of water. To find this, we use a proportion: \[\frac{110 \text{ g sugar}}{100 \text{ g water}} = \frac{x \text{ g sugar}}{25 \text{ g water}}\]

Solve the Proportion

Solve the proportion from Step 2 to find how much sugar can dissolve in 25 g of water:\[x = \frac{110 \times 25}{100} = 27.5 \text{ g sugar}\]

Compare with Actual Sugar Content

The solution has 95 g of sugar in 25 g of water. From Step 3, we calculated that a saturated solution would contain 27.5 g of sugar in 25 g of water.

Determine the Solution's Saturation Level

Since 95 g of sugar is much more than the 27.5 g required for saturation, the solution contains more sugar than the water can dissolve at this temperature. Thus, the solution is supersaturated.

Key concepts

Saturated Solution

A saturated solution refers to a mixture where the maximum amount of solute has been dissolved in the solvent at a given temperature. Imagine a sponge that has absorbed all the water it can hold. Any additional water will simply overflow. Similarly, when a solution reaches saturation, any extra solute will stay undissolved until more solvent or space is provided.
In the context of solubility, if you add sugar to water, there will be a point where no more sugar can dissolve. At this stage, the solution is saturated. For example, at 30°C, water can dissolve up to 110 grams of sugar per 100 grams of water. Attempting to dissolve more than this at the same temperature will result in undissolved sugar remaining visible in the mixture.
This equilibrium is crucial in understanding solution dynamics, as it dictates the maximum concentration possible under stable conditions.

• Occurs when maximum solute is dissolved.
• No more solute can dissolve at the given temperature and pressure.

Unsaturated Solution

An unsaturated solution is one where the solvent can still dissolve more solute at a particular temperature. Think of a sponge that can still absorb more water. The solvent in an unsaturated solution hasn't reached its capacity, so it can take in more solute.
If we reconsider our sugar and water scenario, say you dissolve 50 grams of sugar in 100 grams of water at 30°C. Since this is below the solubility threshold of 110 grams per 100 grams of water, this solution is unsaturated. Adding more sugar will continue to dissolve until saturation is reached.
Unsaturated solutions are flexible and can transition to saturated or even supersaturated states depending on how much solute is added and the temperature maintained.

• Solvent has not reached its full dissolving capacity.
• More solute can be dissolved at the current temperature and pressure.

Supersaturated Solution

A supersaturated solution contains more dissolved solute than would normally be possible at a given temperature. This is like a sponge that has absorbed so much water that it starts to leak unless handled carefully.
In practical terms, achieving a supersaturated solution often involves dissolving solute at a higher temperature, where solubility is greater, and then carefully cooling it without disturbing it. When you dissolve sugar at high temperatures and allow it to cool slowly, more sugar remains dissolved than under normal circumstances, which is what happened in our exercise.
Our provided solution has 95 grams of sugar dissolved in 25 grams of water, while a saturated solution at 30°C would only dissolve 27.5 grams. This vast difference indicates that the solution is supersaturated because it holds far more sugar than the water can typically manage at this temperature.

• Contains more solute than normal saturation levels.
• Achieved under special conditions like temperature change.