R2.1.4 Percentage yield

Percentage Yield - Understanding Efficiency in Chemical Reactions

1. Imagine you’re baking cookies using a recipe that promises 24 cookies.
2. You follow the instructions perfectly, but when you’re done, you only have 20 cookies.
3. What happened? Perhaps some dough stuck to the mixing bowl, or a few cookies broke during baking.

This real-world scenario mirrors what happens in chemical reactions: the amount of product you actually obtain (the actual yield) is often less than the amount you could theoretically produce (the theoretical yield).

What Is Percentage Yield?

It’s calculated using the formula:

$$\text{Percentage Yield}=\frac{\text{Actual Yield}}{\text{Theoretical Yield}}\times 100$$

• Actual Yield: The measured amount of product obtained from the reaction.
• Theoretical Yield: The maximum amount of product expected based on stoichiometry, assuming the reaction goes to completion without any losses.

Factors Affecting Yield

Why don’t reactions always achieve 100% yield? Several factors can reduce the actual yield:

1. Loss of Product During Transfer or Purification

In laboratory experiments, product can be lost during steps like filtration, decanting, or transferring between containers.

2. Side Reactions

Chemical reactions don’t always proceed exactly as planned. Other reactions may occur simultaneously, consuming reactants and forming undesired by-products.

3. Impurities in Reactants

If the reactants are not pure, some of the mass will not contribute to the desired reaction.

Solving Problems Involving Percentage Yield

• Let’s apply these concepts to solve a problem.
• Suppose you’re reacting 5.00 g of magnesium (Mg) with excess hydrochloric acid (HCl) to produce magnesium chloride (MgCl₂) and hydrogen gas (H₂):

$$\text{Mg (s) + 2HCl (aq) → MgCl\_2 (aq) + H\_2 (g)}$$

Step 1: Calculate the Theoretical Yield

1. Determine the molar mass of magnesium:$M(\text{Mg})=24.31\text{g/mol}$.
2. Calculate the moles of magnesium:$$\text{n(Mg)}=\frac{5.00\text{g}}{24.31\text{g/mol}}=0.2057\text{mol}$$
3. Relate moles of Mg to moles of MgCl₂ using the balanced equation: 1 mole of Mg produces 1 mole of MgCl₂. Therefore, the moles of MgCl₂ formed are also $0.2057\text{mol}$.
4. Calculate the mass of MgCl₂:$$\text{m(MgCl₂)}=\text{n(MgCl₂)}\times \text{M(MgCl₂)}=0.2057\text{mol}\times 95.21\text{g/mol}=19.59\text{g}$$
   The theoretical yield is 19.59 g.

Step 2: Calculate the Percentage Yield

Suppose the actual yield of MgCl₂ is 18.00 g. The percentage yield is:
$$\text{Percentage Yield}=\frac{18.00}{19.59}\times 100=91.9$$

Common Mistakes and Tips for Success

Reflection and Broader Implications