Percentage yield and atom economy

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$\%\text{ yield} = \dfrac{\text{actual yield}}{\text{theoretical yield}} \times 100$ — how much product you actually obtained versus the maximum predicted by the equation.

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The amount of product predicted from the balanced equation if the **limiting reactant** reacted completely.

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The amount of product you really obtain — always **less** than theoretical, due to side reactions, reversible reactions and losses.

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Side reactions, reversible reactions not going to completion, and losses during separation/purification.

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$\%\text{ AE} = \dfrac{M(\text{desired product})}{M(\text{all reactants})} \times 100$ — the fraction of reactant atoms ending up in the wanted product.

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Yield = **how much product you made**; atom economy = **how little reactant mass you wasted** as by-products. They are independent.

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**Addition** reactions — all reactants combine into a single product, so there are no by-products.

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Sum the molar masses of **all** reactants, each multiplied by its **coefficient** in the balanced equation.

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Fewer atoms wasted as by-products → less raw material used and less waste to treat → more **sustainable and economical**.

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No — actual yield cannot beat the theoretical maximum. A value over 100% signals an error (e.g. impure/wet product).

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$\text{actual} = \dfrac{\%\text{ yield}}{100} \times \text{theoretical}$.

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Putting only **one** reactant (or forgetting coefficients) on the bottom — you must sum **every** reactant's molar mass.