Solutions and Mixtures — Free Chemistry Review Games.

A solution is a homogeneous mixture where one substance (solute) is dissolved uniformly in another (solvent).

Water is the solvent (present in greater amount) and salt is the solute (dissolved substance).

A substance is soluble if it can dissolve in a particular solvent to form a solution.

Homogeneous mixtures have uniform composition throughout, while heterogeneous mixtures have visibly different components.

A saturated solution contains the maximum amount of dissolved solute at that temperature, so additional solute will not dissolve.

Molarity (M) is a concentration unit defined as moles of solute divided by liters of solution.

For most solid solutes, increasing temperature increases solubility because added energy helps break solute bonds.

A supersaturated solution contains more solute than a saturated solution at the same temperature, achieved by cooling a hot saturated solution.

Polar substances dissolve well in polar solvents, and nonpolar substances dissolve well in nonpolar solvents.

According to Henry's Law, increasing pressure above a liquid increases the solubility of a gas in that liquid.

Colligative properties (boiling point elevation, freezing point depression, osmotic pressure) depend on the concentration of solute particles, not their type.

Dissolved solute particles lower the vapor pressure, meaning the solution must be heated to a higher temperature to reach boiling.

Molarity = moles/liters = 4.0 mol / 2.0 L = 2.0 M.

Osmotic pressure is the minimum pressure required to prevent the flow of solvent through a semipermeable membrane from dilute to concentrated solution.

Moles needed = 0.1 M x 0.5 L = 0.05 mol. Mass = 0.05 mol x 40 g/mol = 2.0 g dissolved in water to a total volume of 500 mL.

Molality is defined as moles of solute divided by kilograms of solvent, which makes it independent of temperature since it uses mass rather than volume. The choice 'Moles of solute per liter of solution' describes molarity, a different concentration unit that does change with temperature due to volume expansion. Students should remember molality is preferred for colligative property calculations because temperature fluctuations do not affect mass-based measurements.

The solute is the substance present in the smaller amount that gets dissolved, which is sugar in this case. Water is the solvent because it is present in the larger amount and does the dissolving, not the 'solute'. A key exam principle is identifying solute versus solvent based on relative quantity, which sets up correct concentration calculations.

An unsaturated solution can still dissolve additional solute at that temperature because equilibrium between dissolved and undissolved solute has not been reached. 'Saturated' is incorrect because a saturated solution holds the maximum amount of solute possible without additional heating or pressure changes. Recognizing these states helps predict whether more solute will dissolve or precipitate out.

Percent by mass is calculated as the mass of solute divided by the total mass of the solution, multiplied by 100 to express it as a percentage. The option dividing solute mass by solvent mass alone ignores the solute's own contribution to the total mass, making that ratio incorrect for percent by mass. This concentration unit is common in labeling household products like saline solutions.

A colloid contains dispersed particles that are larger than those in a true solution but small enough to remain suspended indefinitely due to constant collisions with solvent molecules. The description 'A mixture whose particles settle out over time under gravity' actually refers to a suspension, not a colloid. Students should know colloids exhibit the Tyndall effect, scattering light, which distinguishes them from true solutions.

Gas solubility in liquids generally decreases with increasing temperature because higher kinetic energy allows gas molecules to escape the liquid more easily. The idea that solubility 'increases' with temperature applies to most solid solutes, not gases, so it is the wrong trend here. This is why warm soda goes flat faster than cold soda, a common real-world application of this principle.

Solubility specifically refers to the maximum quantity of a solute that can dissolve in a solvent at a given temperature and pressure, reaching a saturation point. 'Molarity' instead measures the actual concentration of solute present in a solution, not the maximum possible amount. Solubility values are often given in grams per 100 mL of solvent and plotted on solubility curves for exam problems.

Dissolved table salt (NaCl) ionizes fully in water into \(Na^+\) and \(Cl^-\) ions, allowing the solution to conduct electricity, which defines it as an electrolyte. Sugar dissolves as intact molecules without forming ions, so 'Dissolved sugar in water' does not conduct electricity and is a nonelectrolyte. Recognizing ionic versus molecular dissolution is essential for predicting a solution's conductivity and colligative behavior.

Parts per million is used for extremely dilute solutions because it expresses the ratio of solute mass to solution mass on a scale of one million, capturing tiny concentrations meaningfully. Molarity could technically be used but becomes an awkwardly small number for trace-level substances, making 'Molarity (M)' less practical here. Environmental chemistry commonly reports contaminant levels in ppm or parts per billion for this reason.

For most solid solutes, raising the temperature increases the kinetic energy of solvent molecules, allowing them to break apart the solute's lattice structure more effectively and dissolve more of it. 'Decreasing temperature' typically has the opposite effect, reducing the solubility of solids, which is why some solutions form crystals when cooled. Pressure changes have a negligible effect on solid solubility, unlike their strong effect on gas solubility.

\(K_f\) is a solvent-specific constant used in the equation \(\Delta T_f = i K_f m\) to calculate how much the freezing point of a solution drops due to dissolved particles. The boiling point analog is \(K_b\), so the option describing 'the change in boiling point' actually refers to a different constant. Both constants are colligative property constants that depend only on the identity of the solvent, not the solute.

In the dilution formula, \(M_1\) represents the initial, more concentrated molarity before water is added to reduce the concentration. \(M_2\), not \(M_1\), represents 'the final (diluted) molarity' after the dilution has occurred. This formula works because the moles of solute remain constant during dilution, only the volume and concentration change.

A true solution has particles at the atomic, ionic, or small molecular level, which are too small to scatter visible light or be separated by ordinary filtration. A colloid, by contrast, does scatter light due to the Tyndall effect, which rules out 'A colloid' as the answer here. Understanding particle size differences helps classify mixtures into solutions, colloids, and suspensions on the AP exam.

Using \(n = M \times V\), multiplying \(3.0\ \text{mol/L} \times 2.0\ \text{L}\) gives \(6.0\) moles of solute. The value '1.5 moles' would incorrectly result from dividing molarity by volume rather than multiplying them together. Mastering this rearrangement of the molarity formula is essential for solving nearly every concentration-based stoichiometry problem.

Molarity is moles divided by liters, so \(0.50\ \text{mol} \div 0.250\ \text{L} = 2.0\ \text{M}\). The answer '0.5 M' incorrectly treats the volume as though it were 1 L instead of converting 250 mL to 0.250 L first. Careful unit conversion from milliliters to liters is a frequent source of error on concentration problems.

Nonvolatile solute particles occupy some of the surface area of the solution, physically blocking solvent molecules from escaping into the gas phase, thereby lowering vapor pressure as described by Raoult's law. The claim that solute particles 'react chemically with the solvent' is incorrect because vapor pressure lowering is a physical, colligative effect, not a chemical reaction. This same particle-crowding concept underlies boiling point elevation and freezing point depression as well.

Raoult's Law states that the vapor pressure of a solution equals the mole fraction of the solvent multiplied by the pure solvent's vapor pressure, $P_{solution} = X_{solvent}P^{\circ}_{solvent}$. Using the solute's mole fraction instead, as in 'Raoult's Law states $P_{solution} = X_{solute}P^{\circ}_{solvent}$', would give an incorrect and physically meaningless relationship for solvent vapor pressure. This law forms the theoretical basis for vapor pressure lowering as a colligative property.

Mole fraction is moles of solute divided by total moles, so \(2 \div (2+8) = 0.20\). Choosing '0.25' would result from mistakenly dividing solute moles by solvent moles alone rather than by the total moles present. Mole fraction is essential for Raoult's law and must always sum to 1 across all components in a mixture.

Molality is based on the mass of solvent rather than the volume of solution, so it remains constant even as temperature changes and volume expands or contracts, making it ideal for temperature-dependent colligative property calculations. The claim that molarity 'cannot be measured experimentally' is false since molarity is routinely measured and used in many other chemistry contexts. This distinction is a classic AP exam concept testing understanding of why unit choice matters for accuracy.

Glucose is a molecular compound that dissolves as intact molecules without breaking into ions, so its van't Hoff factor is 1, meaning one mole of solute produces one mole of dissolved particles. An answer of '2' would apply to a solute like NaCl that dissociates into two ions per formula unit. The van't Hoff factor directly scales colligative property equations such as \(\Delta T_f = i K_f m\).

$CaCl_2$ dissociates completely into one \(Ca^{2+}\) ion and two \(Cl^-\) ions, producing a total of three particles per formula unit, giving \(i = 3\). An answer of '2' would incorrectly assume only partial dissociation or a 1:1 dissociation ratio like NaCl. Predicting the van't Hoff factor requires counting all ions produced when an ionic compound fully dissociates.

Since only 60 g has dissolved out of a possible 80 g at that temperature, the solution has not reached its maximum solubility and is therefore unsaturated. 'Saturated' would only apply if exactly 80 g were dissolved, matching the maximum indicated by the solubility curve. Reading solubility curves accurately is a key skill for determining a solution's saturation status at a given temperature.

Henry's Law states \(C = kP\), meaning the concentration of dissolved gas is directly proportional to the partial pressure of that gas above the solution's surface. The statement that solubility is 'inversely proportional' to pressure contradicts the direct relationship that Henry's Law establishes and describes the opposite trend. This principle explains why carbonated beverages fizz when opened, since reducing pressure decreases dissolved \(CO_2\) solubility.

Water is a polar molecule that forms strong hydrogen bonds with itself, while oil is nonpolar, so the two substances cannot form favorable intermolecular attractions, causing them to remain separated as immiscible layers. The claim that oil 'reacts chemically with water to form a precipitate' is false because no chemical reaction occurs between oil and water at all. This polarity mismatch is the core reasoning behind the 'like dissolves like' rule for predicting solubility.

Using \(M_1V_1 = M_2V_2\), solving for \(V_1\) gives \(V_1 = \dfrac{(1.5\ \text{M})(300\ \text{mL})}{6.0\ \text{M}} = 75\ \text{mL}\). The choice '150 mL' would result from a calculation error such as dividing incorrectly or mismatching which molarity belongs to which volume. Dilution calculations rely on the principle that moles of solute stay constant while only volume and concentration change.

Dissolved solute particles interfere with the regular packing of solvent molecules into a solid crystal lattice, so a lower temperature is needed to overcome this disruption and allow freezing, which is the mechanism behind freezing point depression. The claim that ethylene glycol 'chemically reacts with water to form a new compound' is incorrect since freezing point depression is a physical colligative effect, not a chemical reaction. This same particle-based disruption explains why salt is spread on icy roads in winter.

Solutions with equal osmotic pressure are described as isotonic, meaning there is no net movement of water across a semipermeable membrane separating them. 'Hypertonic' instead describes a solution with a higher solute concentration and osmotic pressure relative to another solution, which would cause water to flow toward it. This terminology is critical in biology and chemistry for understanding cell behavior in different solution environments.

Since $CaCl_2$ dissociates into three particles (\(i=3\)), a 0.10 M solution produces an effective particle concentration of about 0.30 M, matching the particle concentration of a 0.30 M glucose solution which does not dissociate (\(i=1\)). A '0.10 M solution of glucose' would only have one-third the effective particle concentration, resulting in a much smaller boiling point elevation. Colligative properties depend on total particle concentration, not just the formula concentration of the solute.

Higher solute concentration means more reactant particles are packed into the same volume, increasing the frequency of effective collisions and generally speeding up the reaction rate according to collision theory. The claim that concentration 'always decreases reaction rate due to particle crowding' misrepresents how collision frequency actually works in most solution-phase reactions. This concentration-rate relationship connects solutions chemistry to kinetics, a frequently tested cross-topic link on the AP exam.

The absence of visible residue indicates complete dissolution, and the release of heat energy shows the dissolution process was exothermic, meaning the new solute-solvent interactions released more energy than was required to break the original bonds. The idea that 'the solute did not dissolve at all and simply melted' contradicts the observation of no residue, which indicates the solute is fully dispersed at the molecular level. Recognizing whether dissolution is exothermic or endothermic based on temperature change is an important qualitative skill in solutions chemistry.

First convert grams to moles: \(58.5\,\text{g} \div 58.5\,\text{g/mol} = 1.0\,\text{mol}\), then divide by the volume in liters: \(1.0\,\text{mol} \div 0.500\,\text{L} = 2.0\,\text{M}\). The answer '1.0 M' would result from forgetting to convert 500 mL into 0.500 L before dividing. This two-step process of converting mass to moles before applying the molarity formula is a foundational skill for solution stoichiometry.

In the open beaker, escaped \(CO_2\) gas disperses into the atmosphere rather than accumulating above the liquid, keeping the partial pressure of \(CO_2\) low and continuously driving more dissolved gas out according to Henry's Law and Le Chatelier's principle. The claim about temperature being higher in the open beaker is incorrect since both beakers are stated to be at the same temperature. This dynamic equilibrium concept explains everyday phenomena like flat soda in an uncapped bottle.

Moles of NaOH equal \(20.0\,\text{g} \div 40.0\,\text{g/mol} = 0.50\,\text{mol}\), and dividing by kilograms of solvent, \(0.500\,\text{kg}\), gives \(0.50 \div 0.500 = 1.0\,m\). The value '0.5 m' would occur if a student mistakenly divided moles by 1 kg instead of the actual 0.500 kg of water used. Molality calculations always require converting solvent mass into kilograms before dividing.

Water molecules, being polar, orient their partially negative oxygen atoms toward \(Na^+\) and partially positive hydrogens toward \(Cl^-\), stabilizing the separated ions through ion-dipole interactions that overcome the ionic lattice energy. Hexane is nonpolar and cannot form these stabilizing interactions, which is why the claim that 'hexane molecules are too large' is not the actual reason for poor solubility. This ion-dipole stabilization mechanism is central to explaining why 'like dissolves like' applies to ionic versus nonpolar solvents.

First find moles needed: \(0.400\,\text{mol/L} \times 0.250\,\text{L} = 0.100\,\text{mol}\), then convert to mass: \(0.100\,\text{mol} \times 159.6\,\text{g/mol} = 15.96\,\text{g}\). The value '6.38 g' would result from an arithmetic error such as using the wrong volume or molarity in the initial moles calculation. Preparing a solution of specific molarity always begins with calculating the required moles of solute before converting to a measurable mass.

A semipermeable membrane selectively allows small solvent molecules, typically water, to pass through while blocking larger solute particles, so solvent naturally flows from the less concentrated side toward the more concentrated side to equalize concentration, generating osmotic pressure. The option stating the membrane 'blocks solvent molecules but allows solute particles to pass through' describes the reverse of actual membrane behavior and would not produce osmosis at all. This selective permeability is the defining feature that distinguishes osmosis from simple diffusion.

Rearranging \(\Delta T_b = iK_bm\) gives \(m = \dfrac{1.02}{(1)(0.512)} \approx 2.0\,m\). The value '1.0 m' would result from an arithmetic mistake such as dividing incorrectly or forgetting to isolate \(m\) properly. This rearrangement of the boiling point elevation formula is frequently tested when determining unknown concentrations or molar masses from experimental data.

Since $MgCl_2$ dissociates into three particles per formula unit while glucose does not dissociate at all, the $MgCl_2$ solution has three times the effective particle concentration, causing a greater freezing point depression according to \(\Delta T_f = iK_fm\). The claim that 'both solutions will have identical freezing points since molality is the same' ignores the crucial role of the van't Hoff factor in colligative property calculations. This comparison illustrates why the number of dissolved particles, not just moles of solute, determines the magnitude of colligative effects.

Since moles equal molarity times volume and the volumes are equal, Solution A having four times the molarity of Solution B means it contains four times as many moles of solute, consuming proportionally more reagent in a complete reaction. The claim that 'Solution B will react with more reagent because lower concentration increases reactivity' incorrectly assumes concentration inversely affects the total amount of substance present. This relationship between concentration, volume, and moles underlies solution stoichiometry calculations frequently seen in titration problems.

When solute-solvent attractions are strong, the energy released upon forming new solute-solvent interactions can offset or exceed the energy needed to break apart the solute's original structure and the solvent's intermolecular forces, favoring greater dissolution. The claim that solubility 'depends only on molecular size' ignores the well-established role of intermolecular force compatibility captured by the 'like dissolves like' principle. This energy balance between separating particles and forming new interactions determines whether a dissolution process is thermodynamically favorable.

The mole fraction of B is \(7.0 \div 10.0 = 0.70\), so by Raoult's Law, \(P_B = X_B P^{\circ}_B = 0.70 \times 100\,\text{torr} = 70\,\text{torr}\). The value '30 torr' incorrectly uses the mole fraction of solute A instead of solvent B in the calculation. This calculation demonstrates how vapor pressure contributions in ideal mixtures depend directly on each component's mole fraction.

For \(i=1\), the predicted depression would be \(\Delta T_f = (1)(1.86)(1.00) = 1.86\,^{\circ}\text{C}\), but the observed depression of \(2.79\,^{\circ}\text{C}\) is larger, giving an effective \(i \approx 1.5\), suggesting the compound is partially ionizing despite being labeled a nonelectrolyte. The claim that 'the solute is behaving as expected for a perfect nonelectrolyte with \(i=1\)' contradicts the numerical mismatch between predicted and observed values. Comparing experimental and theoretical van't Hoff factors is a classic hard-level application testing whether students can detect unexpected dissociation behavior.

NaCl contributes \(0.20\,\text{M} \times 1 = 0.20\,\text{M}\) of \(Cl^-\), while $CaCl_2$ contributes \(0.10\,\text{M} \times 2 = 0.20\,\text{M}\) of \(Cl^-\) due to its two chloride ions per formula unit, giving a combined total of \(0.40\,\text{M}\). The value '0.30 M' would result from forgetting to double the chloride contribution from $CaCl_2$'s dissociation. Calculating total ion concentration from mixed electrolytes requires accounting for each compound's dissociation stoichiometry separately before summing.

In concentrated solutions, ions are closer together and can experience attractive interactions that cause some ions to behave as paired units rather than fully independent particles, making the observed colligative effect smaller than the theoretical value predicted using the ideal van't Hoff factor. The claim that 'strong electrolytes stop dissociating completely once molality exceeds 1.0 m' overstates the effect, since dissociation still occurs, just with reduced ionic independence rather than complete cessation. This discrepancy between ideal and real behavior is why chemists distinguish between theoretical and experimentally observed van't Hoff factors at higher concentrations.

Since each formula unit of $PbCl_2$ produces two chloride ions, the molar solubility of $PbCl_2$ equals half the chloride concentration: \(2.0 \times 10^{-2} \div 2 = 1.0 \times 10^{-2}\,\text{M}\). The value '\(2.0 \times 10^{-2}\,\text{M}\)' incorrectly equates the molar solubility directly to the chloride ion concentration without accounting for the 2:1 stoichiometric ratio. Relating measured ion concentrations back to molar solubility using dissociation stoichiometry is a key skill connecting solubility equilibrium to concentration calculations.