Stoichiometry and Solution Chemistry: Moles, Molarity, pH, and Yield
Chemistry calculations connect the macroscopic world of grams and litres to the atomic world of molecules and ions. This guide covers the most essential quantitative relationships in general chemistry: the mole concept, solution concentration, acid-base pH, and reaction yield. Master these and you can handle the majority of first-year chemistry problems.
The Mole and Avogadro's Number
A mole is simply a counting unit, like a dozen but vastly larger: 1 mol = 6.022 × 10²³ particles (Avogadro's number, NA). Converting between moles and particles is straightforward:
particles = moles × NA
Converting between moles and grams uses the molar mass M (g/mol) from the periodic table:
mass (g) = moles × M or moles = mass (g) / M
The Moles to Grams Calculator, the Grams to Moles Calculator, and the Moles to Particles Calculator (Avogadro's Number) automate these three conversions.
Concentration: Molarity and Molality
| Measure | Definition | Formula | Units |
|---|---|---|---|
| Molarity (M) | Moles of solute per litre of solution | M = n / V | mol/L (M) |
| Molality (m) | Moles of solute per kilogram of solvent | m = n / kgsolvent | mol/kg |
| Mass percent (w/w %) | Mass of solute per 100 g of solution | % = (msolute / msolution) × 100 | % |
| PPM | Parts per million by mass or volume | ppm = (msolute / msolution) × 10&sup6; | mg/kg or mg/L |
Use the Molarity Calculator, the Molality Calculator, the Mass Percent Solution Calculator (w/w %), and the PPM Concentration Calculator to convert between these concentration scales.
pH and Acid-Base Chemistry
pH measures the acidity of an aqueous solution on a logarithmic scale:
pH = −log₁₀[H₊O⁺]
Similarly, pOH = −log₁₀[OH⁻], and at 25 °C: pH + pOH = 14. For a strong acid, [H₊O⁺] equals the molar concentration of the acid; for a strong base, [OH⁻] equals its molar concentration.
The pH Calculator, the pOH to pH Calculator, and the Hydronium Concentration to pH Calculator cover all three entry points into pH calculations.
Ideal Gas Law
For an ideal gas, pressure, volume, moles, and temperature are linked by:
PV = nRT
where P is absolute pressure (Pa or atm), V is volume (m³ or L), n is moles, T is absolute temperature (K), and R is the universal gas constant (8.314 J mol⁻¹ K⁻¹ or 0.08206 L·atm mol⁻¹ K⁻¹). At standard temperature and pressure (STP, 0 °C, 1 atm) one mole of any ideal gas occupies 22.4 L. The Ideal Gas Law Calculator (PV = nRT) solves for any one variable when the other three are known.
Percent Composition
The percent composition of an element in a compound shows what fraction of the molar mass that element contributes:
% element = (n × Melement) / Mcompound × 100
For water (H₂O): % H = (2 × 1.008) / 18.015 × 100 = 11.19 %. The Percent Composition Calculator works this out for any compound once you supply the formula.
Reaction Yield
In a chemical reaction, the theoretical yield is the maximum mass of product possible assuming the limiting reagent reacts completely. The percent yield compares the actual experimental result to that maximum:
% yield = (actual yield / theoretical yield) × 100
Losses are inevitable due to incomplete reactions, side products, and transfer losses; a yield above 90 % is generally considered good in the lab. The Theoretical Yield Calculator and the Percent Yield Calculator walk through these calculations step by step.
Worked Example: Preparing a Buffer Solution
You want 500 mL of a 0.25 M NaCl solution. How many grams of NaCl (M = 58.44 g/mol) do you need?
- Moles needed: n = 0.25 mol/L × 0.500 L = 0.125 mol
- Mass needed: m = 0.125 mol × 58.44 g/mol = 7.31 g
Weigh out 7.31 g, dissolve in approximately 400 mL of deionised water, then make up to exactly 500 mL in a volumetric flask.
Common Mistakes
- Confusing molarity and molality. Molarity uses the volume of solution (changes with temperature); molality uses the mass of solvent (temperature-independent). Use molality for colligative properties.
- Using Celsius instead of Kelvin in the ideal gas law. Always convert: T(K) = T(°C) + 273.15.
- Ignoring the limiting reagent. Theoretical yield is based on the reagent that runs out first, not on whichever one you have most of.
- Misidentifying pH scale direction. Lower pH means more acidic (higher [H₊O⁺]); pH 1 is far more acidic than pH 6.
What is the difference between molarity and normality?
Molarity counts moles of solute per litre. Normality counts equivalents per litre — for acids this means moles of H⁺ available per litre. Normality = molarity × n-factor. For HCl, n-factor = 1, so normality equals molarity; for H₂SO₄, n-factor = 2, so a 1 M solution is 2 N.
How do I find the limiting reagent?
Divide the moles of each reactant by its stoichiometric coefficient. The reactant giving the smallest value is the limiting reagent and determines the theoretical yield.
Does the ideal gas law apply to real gases?
It is an approximation that works well at low pressures and high temperatures. At high pressures or low temperatures, use the van der Waals equation or another equation of state for greater accuracy.