Question

The weight of an empty china dish is \(39 \mathrm{~g}\) and when a saturated solution of potassium nitrate is poured into it, its weight is \(108 \mathrm{~g}\) at \(50^{\circ} \mathrm{C}\). After evaporating the solution to dryness, if the weight of the dish along with the crystals is \(72 \mathrm{~g}\) then the solubility of potassium nitrate at \(50^{\circ} \mathrm{C}\) is (a) \(83.9\) (b) \(95.6\) (c) \(91.6\) (d) \(87.4\)

Short answer

Please use the information provided in the step-by-step solution and show your calculations.

Step-by-step solution

1. Calculate the weights of the saturated solution and the crystals

First, we need to find the weights of the saturated solution and the crystals formed after evaporating the solution. We will start by finding the weight of the saturated solution poured (total weight minus empty dish weight), and then, the weight of the potassium nitrate crystals by subtracting the weight of the dish with crystals from the weight of the empty dish. Weight of saturated solution = Weight of dish with solution - Weight of empty dish Weight of potassium nitrate crystals = Weight of dish with crystals - Weight of empty dish

2. Calculate the weight of the water in the saturated solution

Next, we will calculate the weight of the water present in the saturated solution. To do this, we will subtract the weight of the potassium nitrate crystals from the weight of the saturated solution. Weight of water in saturated solution = Weight of saturated solution - Weight of potassium nitrate crystals

3. Calculate the solubility of potassium nitrate

Lastly, we will use the weights of the potassium nitrate crystals and the water in the saturated solution to calculate the solubility of potassium nitrate at 50 degrees Celsius. Solubility is expressed in terms of grams of solute per 100 grams of solvent. Solubility of potassium nitrate (in grams per 100 grams of water) = (Weight of potassium nitrate crystals / Weight of water in saturated solution) × 100

Key concepts

Saturated Solution

A saturated solution is formed when a solute is dissolved in a solvent until no more can be dissolved at a given temperature. At this point, the solution reaches its maximum concentration of the solute, and any additional amount would remain undissolved.
In the context of our problem, when potassium nitrate is added to water, a saturated solution is created at 50°C. This means that the solution holds as much potassium nitrate as possible for that temperature. If any more potassium nitrate were added under these conditions, it would not dissolve but rather settle at the bottom of the container.
To determine if a solution is saturated, you can look for visible undissolved particles of the solute or see if no more dissolves when added.

Potassium Nitrate

Potassium nitrate, with the chemical formula KNO₃, is a white crystalline substance that is highly soluble in water. It is commonly used in fertilizers, food preservation, and as a component in explosives like gunpowder.
In our exercise, potassium nitrate is the solute that forms a saturated solution. Its solubility varies with temperature: typically higher temperatures allow more of the solute to dissolve. At 50°C, a specific maximum amount of potassium nitrate can dissolve in water before reaching saturation.
When solving for its solubility, we need to understand how much potassium nitrate dissolves in a given amount of water at a particular temperature, which helps in the calculation of solution concentration.

Evaporation Process

Evaporation is the process where liquid turns into vapor and leaves behind any dissolved solids. In our exercise, the evaporation process is crucial for separating potassium nitrate crystals from the saturated solution.
By heating the saturated solution, the water component evaporates. As water leaves, the solution becomes more concentrated until eventually forming solid potassium nitrate crystals. This phase change relies on the fact that at high temperatures, water molecules gain sufficient kinetic energy to escape into the air, effectively reducing the volume of liquid and leaving the solute behind.
This process also highlights how evaporation is a practical method for isolating and measuring the solubility of different solutes like potassium nitrate.

Crystal Formation

Crystal formation occurs when the concentration of a solute exceeds its solubility, and the excess solid begins to come out of the solution. In our example, this happens after the evaporation of water from the potassium nitrate solution.
As the water evaporates, the concentration of potassium nitrate increases until it surpasses the solubility limit, causing the potassium nitrate to arrange itself orderly in the form of crystals. These crystalline structures are stable due to the repeating pattern of ions in a lattice, giving crystals their characteristic shapes and making them easy to recognize.
Crystal formation is not only vital in chemistry but also in various industries, as it helps in refining products and obtaining pure forms of substances.