Some Basic Concepts of Chemistry

The mole is the SI unit for amount of substance: one mole is the amount of substance that contains exactly as many elementary entities — atoms, molecules, ions, or any other specified particles — as there are atoms in exactly 12 g of the carbon-12 isotope. This fixed number of entities is the Avogadro constant, $N_A=6.022\times 10^{23}$ per mole, and it is the same number no matter what is being counted: one mole of electrons, one mole of water molecules and one mole of sodium atoms all contain $6.022\times 10^{23}$ entities.

To connect this particle count to a mass that can be weighed, chemistry defines the atomic mass unit (u) as exactly one-twelfth the mass of a single carbon-12 atom. Because most elements occur naturally as a mixture of isotopes, the atomic mass quoted for an element is really an average atomic mass, weighted by each isotope's natural abundance — carbon's atomic mass of 12.011 u reflects the small natural share of heavier ${}^{13}\mathrm{C}$ and ${}^{14}\mathrm{C}$ alongside the dominant ${}^{12}\mathrm{C}$. Molecular mass is the sum of the atomic masses of every atom in one molecule (water, ${\mathrm{H}}_2\mathrm{O}$, is $2(1.008)+16.00=18.02$ u); for ionic solids such as $\mathrm{NaCl}$, which do not exist as discrete molecules, this same sum is called the formula mass instead.

Molar mass is the mass in grams of one mole of a substance, and it is numerically equal to the atomic, molecular or formula mass expressed in u — so water's molar mass is 18.02 grams per mole and $\mathrm{NaCl}$'s is 58.5 grams per mole. This equivalence is what makes the mole useful at the bench: it converts a particle count into a mass on a balance through $n=\frac{m}{M}$ (given mass over molar mass) and $n=\frac{N}{N_A}$ (number of entities over Avogadro's number). Gases add a third route: at STP, one mole of any ideal gas occupies close to the same fixed molar volume, so $n=\frac{V}{V_m}$ also holds.

The recurring NEET trap is assuming that equal masses of two different substances must contain equal numbers of particles. They don't — Avogadro's law guarantees equal numbers of particles only for equal moles, and mass converts to moles only after dividing by molar mass. So equal masses of, say, ${\mathrm{H}}_2$ and ${\mathrm{O}}_2$ contain wildly different numbers of molecules, because their molar masses differ; any question comparing number of molecules or number of atoms between two given masses must be routed through $n=m/M$ first, and only then multiplied by $N_A$ — never compared as masses directly.

A balanced chemical equation is the foundation of stoichiometry: because atoms are neither created nor destroyed (the law of conservation of mass), the coefficients give the exact mole ratio in which reactants combine and products form. For the combustion of methane, $\mathrm{C}{\mathrm{H}}_4(\mathrm{g})+2{\mathrm{O}}_2(\mathrm{g})\to \mathrm{C}{\mathrm{O}}_2(\mathrm{g})+2{\mathrm{H}}_2\mathrm{O}(\mathrm{g})$, the coefficients say that exactly 1 mole of $\mathrm{C}{\mathrm{H}}_4$ reacts with 2 moles of ${\mathrm{O}}_2$ — a ratio fixed in moles, never in mass. Stoichiometry is the set of calculations that uses this mole ratio to connect the amount of any one substance in the equation to the amount of any other, by converting given masses to moles, applying the ratio, and converting back to whatever unit is asked for.

Real reaction mixtures are rarely combined in the exact ratio a balanced equation demands. When reactants are combined in any other ratio, one of them is used up first, stopping the reaction and leaving some of the other reactant unconsumed — the one consumed first is the limiting reagent, and it alone fixes how much product can form, however much of the other, excess reagent remains. To find it, the amount of each reactant supplied is converted to moles and divided by its own coefficient in the balanced equation; whichever reactant gives the smallest such value is the one that runs out first.

For ${\mathrm{N}}_2(\mathrm{g})+3{\mathrm{H}}_2(\mathrm{g})\to 2\mathrm{N}{\mathrm{H}}_3(\mathrm{g})$, supplying nitrogen and hydrogen in any mole ratio other than exactly 1 : 3 guarantees that one of them is limiting. Every downstream calculation — moles of $\mathrm{N}{\mathrm{H}}_3$ formed, and mass of the excess reactant left unreacted — must then be built from the limiting reagent alone, never from whichever reactant's amount was given first or looks larger.

Because real reactions rarely proceed with perfect efficiency, the mass of product actually recovered (the actual yield) is usually less than the mass calculated from the limiting reagent (the theoretical yield). Their ratio, expressed as a percentage, is the percentage yield: (actual yield / theoretical yield) × 100.

The classic NEET trap is identifying the limiting reagent by comparing the raw moles (or raw masses) of the reactants directly, without dividing by their coefficients first. A reactant present in fewer moles is not automatically limiting if the equation also requires less of it — in ${\mathrm{N}}_2+3{\mathrm{H}}_2\to 2\mathrm{N}{\mathrm{H}}_3$, having more moles of ${\mathrm{H}}_2$ than ${\mathrm{N}}_2$ can still leave hydrogen as the limiting reagent, because each mole of ${\mathrm{N}}_2$ demands three moles of ${\mathrm{H}}_2$. Only after scaling each reactant's moles by its own coefficient can the two be compared on common ground.