Solutions, equilibrium and pH

Count the solute in a measured volume

A solution contains a solute distributed through a solvent. Molar concentration, often called molarity (molarità), counts the moles of solute per litre of solution. If a flask holds $n$ moles dissolved in a final volume $V$ in litres, the concentration is $c=n/V$. A concentration of 0.2 mol per litre means a representative half litre contains 0.1 mol. It says how closely the particles are distributed. The total amount also depends on how much solution you have.

Keep the volume of the solution distinct from the volume of solvent poured in. When preparing a solution to a mark on a flask, dissolve the solute first and add solvent until the bottom of the meniscus lies at the mark. The mark specifies the final volume. A problem that gives mass rather than moles requires a separate conversion. Divide the mass in grams by the solute's molar mass in grams per mole and then divide the amount by the final volume in litres.

Decide what survives a dilution

Adding pure solvent to a measured portion of solution leaves the amount of dissolved solute unchanged, provided none reacts or is lost. Before and after dilution (diluizione), that amount is concentration times volume. Thus $c_1V_1=c_2V_2$. Use the volume of the portion actually transferred for the first volume. If you take a pipette full from a large bottle, only the solute in the pipette enters the new flask. The stock bottle's total contents do not enter the equation.

For a ratio of volumes, the units can cancel when both are expressed alike. To calculate an amount in moles directly from molarity, use litres. Predict the direction before calculating. Expanding a sample from 20 mL to 100 mL spreads the same particles through five times the volume and divides their concentration by five. Mixing two solutions that both contain solute needs an extra step. Add the moles supplied by each portion before dividing by the final volume, provided no reaction consumes the solute.

Predict the response of a reversible reaction

In a closed mixture at dynamic equilibrium (equilibrio dinamico), forward and reverse reactions continue at equal rates. Concentrations stay constant over time although individual particles still react. The concentrations of reactants and products need not be equal. Add a reactant while keeping temperature and volume fixed and the immediate composition changes. In a simple reversible reaction the mixture then consumes some of the added reactant and forms more product until the rates again match. It need not consume all of the added material.

For a gas mixture, decreasing volume at fixed temperature raises the partial pressures. The equilibrium shifts towards the side with fewer gas molecules when the two sides have different gaseous coefficient totals. Count only gaseous species for this comparison. A catalyst instead speeds the routes in both directions. An equilibrium mixture with a catalyst has the same equilibrium composition at the same temperature, although a disturbed mixture can settle more quickly.

Read a logarithmic scale

For dilute aqueous solutions in elementary calculations, write $\mathrm{pH}=-\log_{10}[\mathrm{H}^+]$, using the numerical concentration in moles per litre. If the concentration is an exact power of ten, the exponent changes sign. A fall from $10^{-2}$ to $10^{-3}$ mol per litre therefore raises pH from 2 to 3. Each unit corresponds to a factor of ten. A difference of two pH units gives a hundredfold concentration ratio even though the written numbers differ by only two.

A strong monoprotic acid supplies approximately one hydrogen ion per acid molecule in dilute water when the acid's contribution dominates that of water. Under those conditions, a tenfold dilution decreases the hydrogen-ion concentration tenfold. A weak acid dissociates only partially, and dilution changes the degree of dissociation. Applying the strong-acid shortcut to a weak acid can therefore give an incorrect pH. When a question supplies the hydrogen-ion concentration itself, use that number directly.