A-level Chemistry/OCR (Salters)/Yield

Percentage yield formula

There is a simple formula you can use to calculate the percentage yield of a reaction A → B:

$\text{percentage yield}=\frac{m_B\times M_A}{m_A\times M_B}\times 100$

• $m_A$ stands for the mass of substance A in g
• $M_A$ stands for the molar mass of substance A in g mol⁻¹
• $m_B$ stands for the mass of substance B in g
• $M_B$ stands for the molar mass of substance B in g mol⁻¹

In words, this is:

$\text{percentage yield}=\frac{\text{mass of product}\times \text{molar mass of starting material}}{\text{mass of starting material}\times \text{molar mass of product}}\times 100$

This can also be written as:

$\text{percentage yield}=\frac{\text{mass of product}÷\text{molar mass of product}}{\text{mass of starting material}÷\text{molar mass of starting material}}\times 100$

Another way of writing the same this is given below, but this form is a little untidy:

$\text{percentage yield}=\frac{\frac{\text{mass of product}}{\text{molar mass of product}}}{\frac{\text{mass of starting material}}{\text{molar mass of starting material}}}\times 100$

Derivation of formula

Notation

$n_X$ means number of moles of substance X

$m_X$ means mass of substance X

$M_X$ means molar mass of substance X

Definition of yield

$\text{yield}=\frac{n_B}{n_A}$

Definition of percentage yield

$\text{percentage yield}=\frac{n_B}{n_A}\times 100\mathrm{\%}$

Expressing moles in terms of mass and RFM

$n_X=\frac{m_X}{M_X}$, which you may know as $\text{moles}=\frac{\text{mass}}{\text{RFM}}$

therefore, wherever $n_X$ appears, it can be replaced with $\frac{m_X}{M_X}$

thus $n_B=m_B/M_B$

and $n_A=m_A/M_A$

Rewriting the yield formula in terms of mass and RFM

substituting the above equations into the formula for percentage yield

$\text{percentage yield}=\frac{n_B}{n_A}\times 100\mathrm{\%}$

gives

$\text{percentage yield}=\frac{m_B/M_B}{m_A/M_A}\times 100\mathrm{\%}$

which can be rearranged to give

$\text{percentage yield}=\frac{m_B{M}_A}{m_A{M}_B}\times 100\mathrm{\%}$