Q.A solution is prepared by mixing $36\ \text{g}$ of water ($\text{H}_2\text{O}$, molar mass $18.02\ \text{g mol}^{-1}$) with $46\ \text{g}$ of ethanol ($\text{C}_2\text{H}_5\text{OH}$, molar mass $46.07\ \text{g mol}^{-1}$). Calculate the mole fraction of water and of ethanol in the solution.

Only molarity is defined using the volume of the solution, and volume is the one quantity in these definitions that genuinely changes with temperature.

Molarity, $M=\dfrac{n_{solute}}{V_{solution}(\text{L})}$: as temperature rises, the solution expands (volume $V$ increases), so for the same fixed amount of solute the molarity numerically decreases — molarity is temperature-dependent.

Molality, $m=\dfrac{n_{solute}}{\text{mass of solvent (kg)}}$: mass does not change with temperature, so molality of a given solution stays fixed regardless of temperature.

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Molarity of pure water = (mass of 1 L of water) / (molar mass of water), using its density of ~1 g/mL.

Calculation: Take 1 litre (1000 mL) of pure water. Since the density of water is ~1 g/mL, this has a mass of 1000 g.

Moles of water $=\dfrac{1000\text{ g}}{18\text{ g/mol}}=55.55\text{ mol}$

Since this is the number of moles present in 1 litre, the molarity is: …

Concentration terms defined using masses (or moles) rather than the solution's volume are temperature-independent, because mass does not change when a liquid expands or contracts on heating/cooling.

Concentration terms like molarity and normality are defined per unit volume of solution. Since the volume of a liquid changes with temperature (thermal expansion/contraction), these values change slightly with temperature even though the actual amount of solute present is unchanged.

By contrast:

• Molality ($m$) = moles of solute per kilogram of solvent (a mass-based ratio).
• Mole fraction ($x$) = moles of one component divided by total moles of all components (a ratio of amounts of substance). …

Molarity is volume-dependent (moles per litre of solution), so it falls as the solution expands on heating; mass-based measures (molality, mole fraction, mass %) are temperature-independent.

On heating an aqueous solution, the volume of the solution increases (thermal expansion) while the number of moles of solute and the total mass remain unchanged.

• Molarity $= \dfrac{\text{moles of solute}}{\text{volume of solution (L)}}$ — since volume increases, molarity decreases. …

The WHO guideline (safe) limit for copper in drinking water is 2 ppm (2 mg/L).

Background

Concentration in parts per million (ppm) expresses the mass of solute per $10^6$ parts of solution — e.g. 1 ppm = 1 mg of solute per litre of water (since 1 L of dilute aqueous solution ≈ 1000 g). This unit is commonly used for trace pollutant/metal-ion levels in drinking water because the concentrations involved are extremely small.

The specific limit …