Composition, Solutions, and Stoichiometry

This is Unit Three of Chemistry, Part Three: stoichiometry, yield, and analysis. A balanced equation's coefficients give a mole ratio, and that ratio is the only bridge between one substance's amount and another's. Grams of reactant and grams of product relate through moles, never through mass directly — which is why every calculation in this part goes to moles, applies a ratio, and comes back. The same point decides which reactant limits a reaction. The limiting reactant is not the one with the smaller starting mass. It is the one that would produce less product, which you find by converting each reactant separately and comparing what each could make on its own. Then yield. Theoretical yield is a calculated ceiling from the limiting reactant, not a prediction of what a real flask will give. Percent yield is what was actually collected against that ceiling — and a figure above one hundred percent is a measurement or purity problem, not a reaction that beat its own maximum. The part closes on three measurement techniques and a capstone running one reaction from a skeleton equation through to a percent yield. By the end you will be able to do five things. One: say why grams relate only through moles. Two: identify a limiting reactant. Three: read a percent yield. Four: work a titration. Five: say what combustion analysis misses.

Two entries. The ratio a balanced equation encodes, and the three-step conversion that uses it. Both warnings point at the same shortcut — trying to relate masses without passing through moles.

The ratio.

Chem 0471 Mole Ratios from a Balanced Equation

A balanced equation's coefficients give the exact mole ratio in which reactants combine and products form — two moles of hydrogen consuming one of oxygen and producing two of water. Those ratios come only from a correctly balanced equation; an unbalanced one's coefficients give a ratio that misrepresents the reaction.

Mass to mass.

Chem 0474 Stoichiometric Calculations: Mass to Mass

Convert the given mass to moles, apply the balanced equation's mole ratio, then convert back to a mass. Ten grams of hydrogen, divided by its molar mass, gives about four point nine six moles; the two-to-two ratio with water means the same number of moles of water; multiplying by water's molar mass gives about eighty-nine grams. Skipping the mole-ratio step and multiplying masses directly ignores that grams of reactant and grams of product relate through moles, never through mass alone.

Two entries on the reactant that stops the reaction. The definition is straightforward and the identification is not — the warning on both entries is against the intuitive shortcut of comparing starting masses.

The one that runs out.

Chem 0477 Limiting Reactant

The limiting reactant is the one fully consumed first, capping how much product a reaction can form — given excess hydrogen and a smaller fixed amount of chlorine, the reaction stops when chlorine runs out however much hydrogen remains. It is not whichever substance has the smaller starting mass; identity depends on the equation's mole ratio too.

Finding it.

Chem 0480 Determining the Limiting Reactant

Calculate how much of one product each reactant could form entirely on its own, then take whichever yields less. Two grams of silicon with one and a half grams of nitrogen: silicon alone could form about three point three grams of the product, nitrogen alone about three point eight. Silicon yields less, so silicon limits and nitrogen is in excess. Comparing the two starting masses directly and picking the smaller one skips the mole-ratio conversion the determination actually needs.

Three entries. A calculated maximum, the comparison against what was actually obtained, and the procedure. Note that a percent yield over one hundred is treated as diagnostic — it tells you something went wrong in the measurement.

The maximum.

Chem 0483 Theoretical Yield

A reaction's theoretical yield is the maximum amount of product calculable from the limiting reactant using the balanced equation's stoichiometry — once silicon is identified as limiting, its full conversion gives that reaction's ceiling. It is a calculated ceiling, not a prediction of what a real laboratory reaction will actually produce.

Against the ceiling.

Chem 0486 Percent Yield

Percent yield is the actual yield obtained divided by the theoretical yield, as a percentage — fifty grams theoretical against forty-two and a half actual gives eighty-five percent. A percent yield above one hundred signals a measurement or purity problem, such as leftover solvent, rather than a reaction that beat its own ceiling.

Working it out.

Chem 0489 Calculating Percent Yield

Find the theoretical yield from the limiting reactant, then divide the measured actual yield by it and multiply by a hundred. Thirty-three grams of carbon tetrachloride with excess hydrogen fluoride predicts about twenty-six grams of product; if twelve and a half grams are isolated and weighed, the percent yield is about forty-eight. Dividing theoretical by actual instead inverts the ratio and can produce a nonsensical figure well above a hundred.

Two entries on titration. The technique carries one honest caveat about what is actually observed, and the calculation carries a warning against assuming a ratio you have not checked.

The technique.

Chem 0492 Titration

A titration measures an unknown solution's concentration by adding a reagent of known concentration until the reaction's equivalence point is reached — a buret delivering measured volumes of a known base into an acid sample until an indicator changes colour. The observed endpoint and the true equivalence point are not identical in principle, though good design keeps the difference negligible.

The calculation.

Chem 0495 Titration Calculations

Convert the titrant's volume and molarity to moles at the endpoint, apply the balanced reaction's mole ratio, then divide by the unknown sample's own volume. A fifty-millilitre acid sample titrated by about thirty-five millilitres of zero point two five molar base receives about zero point zero zero eight eight moles of base; at a one-to-one ratio the sample held the same, giving about zero point one eight molar. Assuming every acid-base titration is one to one skips checking the equation — a base with two hydroxides needs a different ratio.

Two entries on determining composition by weighing. Both carry a limit worth keeping: one requires a reaction to go to completion, and the other cannot measure one of the elements it is used on.

Weighing a precipitate.

Chem 0498 Gravimetric Analysis

Gravimetric analysis determines a sample's composition by causing a measurable change in mass, often by precipitating and weighing one component — dissolved chloride can be precipitated as silver chloride, filtered, dried and weighed to recover the original chloride content. The precipitating reaction has to go essentially to completion, or the measured mass understates what was present.

Burning a sample.

Chem 0501 Combustion Analysis

Combustion analysis burns a weighed sample completely and weighs the carbon dioxide and water produced. Every carbon atom ends up in the carbon dioxide and every hydrogen in the water, so both elements' masses in the original sample can be recovered from the two product masses and compared back to the starting mass for a percent composition. Oxygen in an oxygen-containing sample cannot be read from those products at all — it is found by subtracting the recovered carbon and hydrogen from the total.

One capstone using nearly every tool in the unit — balancing, oxidation numbers, limiting reactant, theoretical yield and percent yield in one continuous analysis. Its warning is the same one the limiting-reactant entries carry, shown as an actual wrong answer.

The capstone. Skeleton to yield.

Chem 0510 Capstone: From Balanced Equation to Percent Yield

A student reacts fifteen grams of aluminium with thirty grams of iron oxide. She balances the skeleton equation, then checks oxidation numbers — aluminium rises, iron falls — confirming redox. Converting each reactant to moles and applying the two-to-one ratio shows the aluminium could consume more iron oxide than is present, so iron oxide limits and aluminium is left over. That gives a theoretical yield near twenty-one grams of iron; seventeen point eight grams are actually collected, for about eighty-five percent. Comparing fifteen grams against thirty directly would have flagged aluminium as limiting, which is wrong.

Five things to carry out of Part Three, and out of Unit Three. Grams relate to grams only through moles, because a balanced equation's coefficients give a ratio of moles rather than of masses. Every stoichiometric calculation therefore has the same shape: convert to moles, apply the ratio, convert back. And the ratio is trustworthy only if the equation is genuinely balanced. The limiting reactant is not the one with the smaller starting mass. Convert each reactant separately, work out how much of one product each could form entirely on its own, and take whichever gives less. The other reactant is in excess and is left over when the reaction stops. Theoretical yield is a calculated ceiling from the limiting reactant, not a forecast. Percent yield divides the actual measured yield by that ceiling. A figure above one hundred percent is diagnostic rather than impressive — it points to a measurement or purity problem, such as leftover solvent in a weighed product. A titration converts the titrant's volume and molarity to moles, applies the balanced reaction's ratio, and divides by the unknown sample's own volume. The ratio has to come from the actual equation, since not every acid-base pairing reacts one to one. And combustion analysis cannot read oxygen directly, because the oxygen in the carbon dioxide and water produced comes from the burning oxygen as well as from the sample. Carbon and hydrogen are recovered from the products; oxygen is found by subtracting them from the sample's total mass. Unit Four turns to thermochemistry — the energy a reaction takes in or gives out.