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Chapter 13: Problem 23

The solubility of \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3} \cdot 9 \mathrm{H}_{2} \mathrm{O}\) in water is 208 \(\mathrm{g}\) per 100 \(\mathrm{g}\) of water at \(15^{\circ} \mathrm{C}\) . A solution of \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3} \cdot 9 \mathrm{H}_{2} \mathrm{O}\) in water at \(35^{\circ} \mathrm{C}\) is formed by dissolving 324 \(\mathrm{g}\) in 100 \(\mathrm{g}\) of water. When this solution is slowly cooled to \(15^{\circ} \mathrm{C},\) no precipitate forms. (a) Is the solution that has cooled down to \(15^{\circ}\) Cunsaturated, saturated, or supersaturated? (b) You take a metal spatula and scratch the side of the glass vessel that contains this cooled solution, and crystals start to appear. What has just happened? (c) At equilibrium, what mass of crystals do you expect to form?

Short Answer

Expert verified
(a) The solution at 15°C is supersaturated. (b) The process of nucleation occurred when the glass was scratched with the spatula, which led to the appearance of crystals. (c) At equilibrium, 116g of crystals are expected to form.

Step by step solution

01

Determine the mass of solute in a saturated solution at 15°C

To do this, we will use the given solubility of the salt: 208g per 100g of water. So, in a saturated solution at 15°C, there will be 208g of solute dissolved in 100g of water.
02

Analyze the solution at 35°C

We are given that at 35°C, 324g of salt is dissolved in 100g of water. Meanwhile, the solubility at 15°C is 208g of solute per 100g of water.
03

Determine the state of the solution at 15°C

As the solution cools down to 15°C, the solubility decreases to 208g/100g of water. The salt remains dissolved in the solution, so it is now a supersaturated solution because it contains more solute than the saturation point at 15°C. Answer (a): The solution at 15°C is supersaturated.
04

Scratch the glass and explain crystals appearing process

When the glass is scratched with the spatula, it introduces small disturbances to the supersaturated solution, providing nucleation sites where the excess solute can attach to and start crystallizing. This is known as nucleation, which is the initial event that leads to crystal growth when the conditions of a supersaturated solution are altered. Answer (b): The process of nucleation occurred when the glass was scratched with the spatula, which led to the appearance of crystals.
05

Calculate the mass of crystals expected at equilibrium

In a saturated solution, there would be 208g of solute in 100g of water at 15°C. Since the solution contains 324g of solute, the difference between these values represents the mass of crystals expected to form at equilibrium: Mass of crystals = 324g (initial) - 208g (saturated amount at 15°C) = 116g Answer (c): At equilibrium, 116g of crystals are expected to form.

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Most popular questions from this chapter

Compounds like sodium stearate, called "surfactants" in general, can form structures known as micelles in water, once the solution concentration reaches the value known as the critical micelle concentration (cmc). Micelles contain dozens to hundreds of molecules. The cme depends on the substance, the solvent, and the temperature. At and above the cmc, the properties of the solution vary drastically. (a) The turbidity (the amount of light scattering) of solutions increases dramatically at the cmc. Suggest an explanation. (b) The ionic conductivity of the solution dramatically changes at the cmc. Suggest an explanation. (c) Chemists have developed fluorescent dyes that glow brightly only when the dye molecules are in a hydrophobic environment. Predict how the intensity of such fluorescence would relate to the concentration of sodium stearate as the sodium stearate concentration approaches and then increases past the cmc.

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