Ideal Solutions and Mixing

Introduction

An ideal solution is a model in which each volatile component follows Raoult's law over the full range of liquid composition. The model predicts a linear total-vapour-pressure relation and, for ideal mixing at fixed temperature and pressure, no enthalpy or volume change from mixing pure liquids. Entropy can still rise, making mixing favourable. “Ideal” describes a precisely defined approximation, not a claim that molecules exert no attractions.

Core explanation

For a binary ideal solution, pA = xA pA° and pB = xB pB° at equilibrium. These equations hold for every composition from pure A to pure B in the ideal model. Total pressure is their sum. A real mixture may obey them approximately over a narrow range or near one pure end while deviating elsewhere. Showing one pressure measurement close to an ideal prediction does not prove ideality across all compositions.

The molecular picture is that interactions between unlike molecules A–B are sufficiently similar, on average, to interactions among like molecules A–A and B–B. Replacing neighbours during mixing then causes no net heat change in the ideal model: ΔmixH = 0. Likewise the ideal mixing-volume change ΔmixV = 0, so volume of the final mixture equals the sum of the initial pure-liquid volumes at the same stated temperature and pressure. These zero changes are model consequences, not statements that individual intermolecular attractions have vanished.

Even with ΔmixH = 0, mixing can be thermodynamically favourable. For distinguishable components, mixing generally increases the number of possible arrangements and gives ΔmixS > 0. At fixed temperature and pressure, ΔmixG = ΔmixH − TΔmixS = −TΔmixS < 0 for the ideal mixture. The model predicts a decrease in Gibbs energy without requiring heat release. This contrasts with a common misconception that a process must be exothermic to occur spontaneously.

In a real mixture, A–B attractions may differ from the average like–like interactions. If they are weaker, molecules can escape the liquid more readily and vapour pressure can lie above Raoult's prediction. If they are stronger, pressure can lie below. Mixing may also warm, cool, expand or contract. The sign of one measured quantity can support a molecular interpretation, but liquid structure and specific interactions can be complicated; avoid presenting a single bond-strength slogan as a full quantitative model.

An example of nearly ideal behaviour is often sought among chemically similar liquids, such as certain pairs of nonpolar hydrocarbons with comparable molecular sizes. “Nearly” matters: no measured liquid mixture is required to satisfy the equations exactly at every composition and temperature. Aqueous mixtures of strongly different substances can be markedly nonideal. Ideal equations are therefore a reference baseline against which data are compared, not a universal property of anything called a solution.

Mixing volume illustrates why solution volume cannot always be obtained by adding input liquid volumes. A real mixture may contract, so 50 mL of one liquid plus 50 mL of another need not give 100 mL final solution. This is exactly why molarity must use measured final volume. Under the ideal solution model ΔmixV is zero, but importing that assumption into an unrelated real concentration problem can introduce an error.

Step-by-step reasoning

1. State whether the problem assumes ideal behaviour or gives measured data. 2. For an ideal binary liquid, use Raoult's law separately for each component. 3. At fixed temperature and pressure, set ideal ΔmixH and ΔmixV to zero. 4. Recognise positive mixing entropy and negative ideal mixing Gibbs energy. 5. Compare any measured heat, volume or vapour-pressure deviation with the baseline before inferring molecular interactions.

Visual explanation

Sketch three small boxes labelled pure A, pure B and mixed A+B. Draw similar-sized contact lines between A–A, B–B and A–B in the mixed box. Below, show ΔmixH = 0 and ΔmixV = 0, but ΔmixS > 0 and ΔmixG < 0 at positive temperature. Beside the boxes, draw a straight total-pressure line between pB° and pA°.

Real-world analogy

If two groups exchange seats and everyone finds the new neighbours about as comfortable as the old ones, no extra heating or room space is needed simply from the rearrangement. Yet there are more mixed seating patterns than separated ones. This resembles zero ideal enthalpy and volume changes plus favourable mixing entropy; real molecular interactions still have physical energy.

Real-world example

When engineers compare measured vapour pressure of a solvent blend with the ideal straight-line prediction, the ideal model acts as a baseline. Close agreement can simplify a preliminary calculation. A systematic curve above or below the line signals that measured vapour–liquid data should replace the ideal assumption in a precise separation calculation.

Why?

Why can mixing be favourable with ΔmixH = 0? The entropy of distributing distinguishable molecules among many arrangements is positive. In ΔmixG = ΔmixH − TΔmixS, the negative −TΔmixS term then lowers Gibbs energy.

Common misconception

“Ideal means molecules do not attract each other.” An ideal liquid mixture still has intermolecular attractions. The approximation says unlike and like interaction effects balance suitably so Raoult's law and zero ideal mixing enthalpy and volume result.

Worked example

Pure liquids A and B have ideal-reference vapour pressures of 80 and 40 kPa at one temperature. Mix them to liquid xA = 0.25. Ideal partial pressures are pA = 20 kPa and pB = 0.75 × 40 = 30 kPa, so total is 50 kPa. If this mixture is formed from separate pure liquids at fixed temperature and pressure under the ideal model, ΔmixH = 0 and ΔmixV = 0, while ΔmixS > 0 for a genuine mixture. A measured total of 55 kPa would be a positive pressure deviation, so the mixture would not meet the ideal model exactly at that composition.

Quick check

1. Does an ideal solution necessarily have zero entropy change on mixing? Answer: No. Ideal mixing generally increases entropy even though its ideal mixing enthalpy and volume changes are zero.

Exam focus

Give the operational Raoult-law definition and the ideal ΔmixH = 0, ΔmixV = 0 results with their fixed-condition context. Explain favourable mixing through entropy and avoid saying zero heat means no molecular forces.

Advanced insight

Ideal chemical potentials take the form μi = μi° + RT ln xi. Since xi lies between zero and one in a genuine mixture, ln xi is negative. The resulting chemical-potential decrease encodes the entropy-driven mixing effect. Real mixtures replace xi with activity ai, so activity coefficients measure departure from ideal composition behaviour.

Summary

An ideal solution obeys Raoult's law across composition. Its ideal mixing enthalpy and volume changes are zero, but mixing entropy is positive and Gibbs energy decreases. Real mixtures can deviate because unlike molecular interactions differ, making the ideal model a benchmark rather than an automatic fact.

Practice questions

1. If ΔmixH = 0 for ideal mixing, must ΔmixG equal zero? Answer: No. ΔmixS > 0 gives ΔmixG = −TΔmixS < 0 at positive temperature. 2. What total ideal pressure follows from pA° = 60 kPa, pB° = 20 kPa and xA = 0.50? Answer: 0.50(60) + 0.50(20) = 40 kPa. 3. Does a real 50 mL plus 50 mL liquid mixture always occupy 100 mL? Answer: No. Real mixing volume can differ from zero, so final volume should be measured.