States of matter, gases, solutions and solubility

States of matter, gases, solutions and solubility

Particles and changes of state

The particle model links states to motion, spacing and attractive interactions. Solid particles vibrate around comparatively fixed positions, liquid particles remain close but change neighbours and gas particles move through much larger average separations. Melting, freezing, boiling, condensation and sublimation alter arrangement and energy without necessarily changing chemical identity. A heating curve can show a level region during a phase change at fixed pressure because supplied energy changes the microscopic arrangement rather than temperature. Brownian motion of suspended particles supports molecular motion but is not a direct view of individual gas molecules. Diffusion arises from random motion and concentration differences, while bulk convection can also move substances.

Gas pressure and absolute temperature

Gas particles striking a wall transfer momentum, producing pressure. For a fixed amount at constant temperature, Boyle's law gives p₁V₁ = p₂V₂. For fixed amount at constant pressure, Charles's law gives. At fixed volume, p/T is constant. Temperature must be in kelvin: approximately for school calculations. A gas at 27°C is near 300 K, not 27 K. Use absolute pressure if gauge readings are involved. State which variables remain fixed before using a proportionality; changing gas amount or allowing heating during compression can invalidate a simplified comparison.

Combined gas law and molar volume

For fixed amount, pV/T is constant. The ideal-gas equation also includes amount. With units require pressure in pascals, volume in m³, temperature in K and amount in mol. A volume of 1 dm³ equals 10⁻³ m³. The molar volume RT/p depends on temperature and pressure, so use the value given in a question rather than assuming 22.4 or 24 dm³/mol under every condition. Equal ideal-gas volumes at the same temperature and pressure contain equal amounts, regardless of whether the gas particles are atoms or molecules.

Partial pressure and diffusion rates

For a nonreacting ideal mixture, total pressure is the sum of component partial pressures. A component's partial pressure equals its mole fraction times total pressure. When a gas is collected over water, subtract the water-vapour pressure to find dry-gas pressure if the data are supplied. Under comparable conditions, Graham's law relates suitable gas diffusion or effusion rates inversely to the square root of molar mass. A gas with one quarter the molar mass has twice the rate in that ideal comparison. Define the ratio in words before substituting, because reversing the mass ratio is a common error. Real mixing, flow and apparatus effects can limit a simple rate interpretation.

What a solution contains

A solution is a homogeneous mixture at the molecular or ionic scale. The solvent is the dissolving medium and solute the dissolved component in the stated description. Dissolving does not always involve ion formation: sugar molecules can disperse in water without becoming the same kind of mobile ions produced by sodium chloride. An electrolyte solution conducts because it contains mobile ions; conductivity also depends on concentration, ion mobility and temperature. A suspension contains larger dispersed particles and can settle or be filtered differently. A colloid occupies an intermediate range in the school classification and can scatter light, so not every apparently uniform mixture is a true molecular solution.

Concentration and dilution

Amount concentration in mol/dm³ when volume is in dm³. Mass concentration is m/V in g/dm³ and is converted to amount concentration using molar mass. A solution containing 5.85 g sodium chloride in a final volume of 500 cm³ has 0.100 mol in 0.500 dm³ if molar mass is 58.5 g/mol, giving 0.200 mol/dm³. Final solution volume is not automatically the volume of solvent poured in before dissolution. For simple dilution, solute amount is conserved, so c₁V₁ = c₂V₂. Dilution lowers concentration but does not change the total number of solute particles if no reaction or loss occurs.

Solubility and saturation

Solubility describes the maximum amount of a substance that dissolves under stated temperature and pressure conditions, with a specified solvent amount and unit convention. A saturated solution is in equilibrium with the maximum dissolved amount at those conditions; an unsaturated solution can dissolve more. A supersaturated solution contains more dissolved solute than the stable equilibrium amount and can crystallise when disturbed or seeded. Stirring and reducing particle size can speed dissolving but do not necessarily change equilibrium solubility. Heating increases the solubility of many solids, but not every substance follows that trend. Gas solubility commonly decreases on warming and increases with its partial pressure under suitable conditions.

Reading solubility curves

First inspect whether the graph gives grams per 100 g water, grams per 100 g solution or another convention. Those denominators are not interchangeable. If solubility is 60 g per 100 g water at 80°C and 20 g per 100 g water at 20°C, cooling a saturated solution containing 100 g water can crystallise 40 g solute, assuming no solvent loss and appropriate equilibrium. For 50 g water the amounts halve. Dissolved mass remaining must be based on the final solvent amount. A crystallisation yield question may also need water of crystallisation or hydration data, so use the exact stated chemical formula.

Qualitative colligative ideas and practical preparation

Dissolved particles can lower a solvent's vapour pressure, raise boiling temperature or lower freezing temperature under suitable dilute-solution conditions. The size of the effect depends mainly on particle amount in the ideal treatment, while dissociation can increase particle count. These ideas explain why a solution's boiling point differs from pure solvent; they do not establish a universal safe household application. To prepare a standard solution, accurately weigh the appropriate pure substance, dissolve it, transfer quantitatively and make up to the calibration mark in a volumetric flask. Mix thoroughly. The correct volume is the flask's final solution volume at its calibration conditions.

Self-check with explanations

A 200 cm³ gas sample at 100 kPa becomes 250 cm³ at constant temperature, so new pressure is 80 kPa. A 0.20 mol solute amount in 250 cm³ solution gives 0.80 mol/dm³ because 250 cm³ is 0.250 dm³. If 30 g solute dissolves per 100 g water at the starting temperature and 10 g per 100 g water remains dissolved at the final temperature, a sample containing 200 g water can yield 40 g crystals under the stated no-loss model. In each calculation, identify whether the denominator is gas volume, solution volume or solvent mass; all three appear in this unit but mean different things.