Molarity and Solubility Practice

Molarity and Solutions: Problem Set Overview

We have 14 ready-to-use problem sets on the topic of Molarity and Solutions. These problem sets focus on the use of the concept of concentration (most specifically molarity) in the analysis of situations involving solution formation, dilution, and solution stoichiometry. Problems will range from the very easy plug-and-chug to the more difficult analysis of reactions involving solutions.

Solution, Solute, Solvent

A solution is a homogeneous mixture of two or more substances. In describing it as homogeneous, we mean that the composition of the two or more substances is uniform or the same throughout the bulk of the solution. In this unit, most solutions will be aqueous solutions. In an aqueous solution, a substance is dissolved in water. We refer to water as the solvent and the substance that is dissolved in it is referred to as the solute. In most instances, the solute will be a solid that is dissolved into the water to form the aqueous solution. The dissolved solid is uniformly distributed throughout the bulk of the water, making the aqueous solution a homogeneous mixture.

Solubility Curves

Not all solids dissolve in equal amounts in water. You may have noticed that a tablespoon of table salt (NaCl) easily dissolves in a cup of water. After a little stirring, the table salt is dissolved and distributed uniformly throughout the water. A second and even a third tablespoon can often be dissolved in the same cup with little difficulty. On the other hand, a tablespoon of sucrose or granulated sugar (C12H22O11) would not readily dissolve in the same cup of water. After stirring, you might noticed some undissolved crystals of sucrose at the bottom of the glass. If you were lucky enough to dissolve the first tablespoon of sucrose, it would be unlikely that a second and a third tablespoon could be dissolved in the same way that the table salt dissolved. This illustrates that not all solids dissolve in equal amounts in water.

When a solid solute is dissolved in water, the water eventually becomes saturated with the solute. The water can no longer hold more dissolved solute particles in the solution. Adding additional solute will result in undissolved solid accumulating at the bottom of the container. We say that the solution is saturated. A saturated solution contains the maximum amount of solute that the solvent can hold at that specific temperature. The solubility of a solute is a quantity that describes the maximum amount of solute that can be dissolved in a specific amount of solvent. For an aqueous solution, this quantity is usually expressed in units of grams of solute per 100.0 grams of water.

As mentioned, not all solids dissolve in equal amounts in water. In other words, different solids have a different solubility. Solubility also depends upon temperature. For most solid solutes, an increase in temperature results in an increase in the solubility of that solid solute. Put another way, more solid can be dissolved in hot water than in cold water. For some solid solutes, the effect of temperature upon the solubility is quite dramatic. For other solids, increases in temperature has a rather small effect upon the solubility. A Solubility Curve is a graph showing the solubility of a solute as a function of temperature. The graph at the right shows the solubility curve for several solutes in water. Each line is labeled with a chemical formula to denote the solid solute that it refers to. Note that the units for solubility (along the vertical axis) are grams of solute per 100 grams of water. And note that the temperature units are °C. In nearly all instances, the lines on the graph show a noticeably positive slope. This agrees with the general trend that increasing the temperature will increase the solubility of a solid solute. The one line on the graph that shows a negative slope is the pink line in the bottom left of the graph. This is the solubility curve for SO2 - a gas. For gases, the solubility in water shows a different pattern as for solids; increasing temperatures result in decreasing solubility of the gas.

By using axis values on a solubility curve, one can determine the solubility of the various solids at a specific temperature. Bear in mind that the solubility refers to the maximum amount of solid that can be dissolved in 100 grams of water at that particular temperature. It describes the amount of solute that can be dissolved to form a saturated solution. One can always add less solid than the saturation amount. In such a case, the solution would be described as an unsaturated solution. In saying that it is unsaturated, we mean that you could continue to add more solid and dissolve it in the aqueous solution.

Consider the solute NH4Cl (the light blue line). At a temperature of 90°C, its solubility is 70.0 grams per 100.0 grams of water. At this temperature,100.0 grams of water could hold as much as 70.0 grams of NH4Cl. If 30.0 grams of NH4Cl is added to 100.0 grams of water at this temperature, the solution would be unsaturated. An additional 40.0 grams of NH4Cl could be added to the 30.0 grams of NH4Cl that is already dissolved in the solution. If that were to occur, then the solution would become saturated (filled up) with the NH4Cl solute.

Now suppose that the saturated solution of NH4Cl at 90°C is slowly cooled down to 30.0°C. From the curve for NH4Cl, we notice that the solubility decreases to a value of 40.0 grams per 100.0 grams of water. That is to say, 100.0 grams of water holds 30.0 grams less solute at 30.0°C compared to 90.0°C. And so a saturated solution that is cooled down from 90°C to 30°C is overly-saturated. We use the phrase supersaturated to describe such a solution. The 100.0 grams of water is holding more solute than it actually is able to hold. It would be analogous to me putting on a shirt at age10-years old and not taking it off for the next five years. As I grow, the shirt gets filled out (saturated) and then a year later super-saturated. Eventually that shirt is going to burst at its seams. Admittedly, that's a bit of an odd analogy … but the idea is that as the solution is cooled down, it is eventually going to have to release some solid. It's going to burst at the seams and the 30.0 grams of extra solid is going to be released out of the solution and appear as undissolved solid. Supersaturated solutions are unstable solutions and will readily revert back to saturated solutions by allowing the additional solid to precipitate inside the container. The only way to produce a supersaturated solution is to saturate the water at a high temperature and then to slowly allow the solution to cool down to a lower temperature where the solubility is less.

Concentration: Mass Percent

The concentration of an aqueous solution describes how much solute is dissolved in a certain amount of the solution. There are a variety of ways to describe the concentration. One of those ways is the mass percent. Mass percent composition describes the mass of solute (in grams) per mass (in grams) of solution on a percent basis. The equation is …

% Solute = ( grams of solute / grams of solution ) * 100.0

Suppose that 10.0 grams of NaCl are dissolved in 100.0 grams of water. The total mass of the solution would be the mass of the solute (NaCl, 10.0 g) plus the mass of the solvent (H2O, 100.0 g). The solution would have a mass of 110.0 grams. The mass percent of NaCl in the aqueous solution would be …

% NaCl = ( 10.0 g / 110.0 g ) * 100

% NaCl = 9.09% (by mass)