General Chemistry: Solutions and Solubility

Solutions are the workhorses of chemistry, forming the basis for countless reactions in labs, biological systems, and industrial processes. Understanding how substances dissolve and how their concentrations are expressed is essential for predicting reaction outcomes, designing pharmaceuticals, and even explaining everyday phenomena like why roads are salted in winter or how our kidneys regulate water balance.

Defining Solutions and Measuring Concentration

A solution is a homogeneous mixture composed of two or more substances. The substance present in the lesser amount is the solute, and the substance that dissolves the solute is the solvent. In most cases, water is the solvent, making an aqueous solution. The quantitative description of a solution's composition is its concentration.

The most common unit is molarity (M), defined as the number of moles of solute per liter of solution: $M=\frac{n}{V}$, where $n$ is moles of solute and $V$ is the total volume of the solution in liters. For example, if you dissolve 0.5 moles of sodium chloride (NaCl) in enough water to make 2.0 L of solution, the molarity is $M=\frac{0.5\text{ mol}}{2.0\text{ L}}=0.25\text{ M}$.

Molarity is temperature-dependent because volume can change with temperature. When this is a concern, molality (m) is used. Molality is defined as moles of solute per kilogram of solvent: $m=\frac{n}{\text{kg solvent}}$. Since mass is temperature-independent, molality is a stable concentration unit. For instance, a solution made by dissolving 1.0 mol of sugar in 2.0 kg of water has a molality of 0.50 m.

A fundamental laboratory skill is performing a dilution, which decreases concentration by adding more solvent. The key relationship is $M_1{V}_1=M_2{V}_2$, where $M_1$ and $V_1$ are the molarity and volume of the concentrated stock solution, and $M_2$ and $V_2$ are the molarity and volume of the diluted solution. If you have 100 mL of a 6.0 M HCl solution and need 500 mL of a 1.0 M solution, you can check if it's possible: $(6.0\text{ M})(0.100\text{ L})=0.60\text{ mol}$ of HCl available. The desired solution requires $(1.0\text{ M})(0.500\text{ L})=0.50\text{ mol}$. Since you have enough solute, you would calculate the volume of stock needed: $V_1=\frac{M_2{V}_2}{M_1}=\frac{(1.0)(0.500)}{6.0}=0.0833\text{ L}$ or 83.3 mL. You would carefully measure 83.3 mL of the 6.0 M stock and add enough solvent (water) to reach a final total volume of 500 mL.

Solubility: Rules and Governing Factors

Solubility is the maximum amount of solute that can dissolve in a given amount of solvent at a specified temperature and pressure, forming a saturated solution. Predicting whether an ionic compound will dissolve in water is streamlined by a set of empirical solubility rules. Key rules include: all common salts of Group 1 metals (Li⁺, Na⁺, K⁺) and ammonium (NH₄⁺) are soluble; all nitrates (NO₃⁻), acetates (CH₃COO⁻), and perchlorates (ClO₄⁻) are soluble; most chlorides (Cl⁻), bromides (Br⁻), and iodides (I⁻) are soluble, except those of Ag⁺, Pb²⁺, and Hg₂²⁺; most sulfates (SO₄²⁻) are soluble, except those of Ba²⁺, Sr²⁺, Pb²⁺, and Ca²⁺ (CaSO₄ is slightly soluble); most hydroxides (OH⁻) and sulfides (S²⁻) are insoluble, except those of Group 1 and the heavier Group 2 metals.

Solubility is not a fixed constant; it is influenced by several factors. For solid solutes in liquid solvents, solubility typically increases with temperature. This principle is used in recrystallization purification techniques. For gaseous solutes, solubility decreases with increasing temperature (which is why a cold soda fizzes more than a warm one) and increases with increasing pressure above the solution, as described by Henry's Law. The nature of the solute and solvent also plays a crucial role, summarized by the adage "like dissolves like." Polar and ionic solutes tend to dissolve in polar solvents like water, while nonpolar solutes dissolve in nonpolar solvents like hexane.

Colligative Properties of Solutions

Colligative properties depend solely on the number of solute particles in a solution, not on their chemical identity. They are powerful tools for determining molar masses and understanding biological and physical processes.

The presence of a nonvolatile solute lowers the vapor pressure of the solvent. For an ideal solution, this is quantified by Raoult's Law: $P_{\text{solution}}={\chi }_{\text{solvent}}{P}_{\text{solvent}}^{\circ }$, where $\chi$ is the mole fraction of solvent and $P^{\circ }$ is the vapor pressure of the pure solvent. This vapor pressure lowering leads directly to two other properties.

Boiling point elevation occurs because a higher temperature is needed for the solution's vapor pressure to reach atmospheric pressure. The increase in boiling point ($\Delta T_b$) is given by $\Delta T_b=i{K}_{b}m$, where $K_b$ is the ebullioscopic constant specific to the solvent, $m$ is the molality, and $i$ is the van't Hoff factor (the number of particles one formula unit of solute yields in solution). For water, $K_b=0.512\text{ °C/m}$. A 1.00 m NaCl solution ($i\approx 2$ due to dissociation into Na⁺ and Cl⁻) would have $\Delta T_b\approx (2)(0.512)(1.00)=1.02\text{ °C}$, boiling at 101.02 °C.

Freezing point depression happens because the solute disrupts the orderly formation of the solid solvent. The decrease in freezing point ($\Delta T_f$) is $\Delta T_f=i{K}_{f}m$. For water, $K_f=1.86\text{ °C/m}$. This is why salt melts ice on roads and why antifreeze (ethylene glycol) is added to car radiator fluid. To find the freezing point of a solution made with 685 g of ethylene glycol (C₂H₆O₂, molar mass 62.07 g/mol) in 2005 g of water, first calculate molality: moles of solute = $685\text{ g}/62.07\text{ g/mol}=11.04\text{ mol}$; mass of solvent = 2.005 kg; $m=11.04/2.005=5.51\text{ m}$. Since ethylene glycol is molecular, $i=1$. Then $\Delta T_f=(1)(1.86)(5.51)=10.2\text{ °C}$. The solution freezes at -10.2 °C.

Osmotic pressure ($\Pi$) is the pressure required to prevent the net flow of solvent across a semipermeable membrane from a pure solvent into a solution. It is a particularly sensitive colligative property, crucial in biology. It is calculated using $\Pi =iMRT$, where $M$ is molarity, $R$ is the ideal gas constant (0.08206 L·atm/mol·K), and $T$ is temperature in Kelvin. A 0.10 M NaCl solution at 25 °C (298 K) has an osmotic pressure of $\Pi \approx (2)(0.10\text{ M})(0.08206\text{ Lcdotpatm/molcdotpK})(298\text{ K})=4.9\text{ atm}$.

Common Pitfalls

1. Confusing Molarity and Molality: The most frequent error is using volume when you need mass or vice versa. Remember, molarity uses liters of solution, while molality uses kilograms of solvent. In concentrated solutions or for precise physical property work, these values differ significantly.
2. Misapplying the Dilution Formula: A critical mistake is using $M_1{V}_1=M_2{V}_2$ for calculations involving a reaction or for converting between molarity and molality. This formula only applies to diluting a stock solution with pure solvent. Also, ensure $V_1$ and $V_2$ are in the same units.
3. Ignoring the van't Hoff Factor ($i$): When calculating colligative properties for ionic compounds, forgetting to account for dissociation will give you an answer that is off by a factor of 2, 3, or more. For molecular solutes like sugar, $i=1$. For NaCl, $i$ approaches 2; for CaCl₂, it approaches 3. However, note that $i$ is often less than the theoretical maximum due to ion pairing in concentrated solutions.
4. Misunderstanding Solubility Limit Calculations: When a problem states a compound is dissolved in a volume of water, the mass of the solvent is not necessarily the same as the mass of that volume of water (1 mL of water = 1 g only at 4°C, but it's a safe approximation). More importantly, in saturated solutions, any added solute will remain undissolved. Calculations must use the solubility limit (e.g., grams per 100 g water) as a conversion factor, not assume all the solid present has dissolved.

Summary

• Concentration is quantitatively described by molarity (mol/L solution) for most purposes and molality (mol/kg solvent) for temperature-independent studies. Dilutions are performed using the formula $M_1{V}_1=M_2{V}_2$.
• Solubility, the maximum dissolvable amount, is predicted by general rules for ionic compounds and is strongly influenced by temperature, pressure (for gases), and the "like dissolves like" principle of molecular polarity.
• Colligative properties—vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure—depend on the number of solute particles present. Their magnitudes are calculated using formulas that incorporate the van't Hoff factor ($i$), molality or molarity, and constants specific to the solvent.
• Mastery of this topic requires careful attention to units, a clear distinction between solvent and solution, and correct application of particle count ($i$) in colligative property calculations.