Concentration, Yield and Atom Economy
Concentration, yield and atom economy apply the mole to solutions and to the efficiency of industrial reactions. Percentage yield compares the mass of product actually obtained with the maximum theoretically possible from a balanced equation, while atom economy measures how much of the mass of the reactants ends up as the desired product, so a reaction can have a high yield yet a poor atom economy if it produces large amounts of by-product.
Method
- Convert volumes to cubic decimetres before substituting: divide the volume in cubic centimetres by 1000, so 25 cubic centimetres is 0.025 cubic decimetres.
- Use concentration in moles per cubic decimetre = moles / volume in cubic decimetres, and its rearrangement moles = concentration x volume.
- Convert between the two concentration units with the relative formula mass: concentration in grams per cubic decimetre = concentration in moles per cubic decimetre x Mr.
- For a titration calculation, follow four fixed steps: moles of the known solution = concentration x volume, use the mole ratio in the balanced equation to find the moles of the unknown, divide by the unknown's volume in cubic decimetres, and multiply by Mr if the answer is wanted in grams per cubic decimetre.
- For percentage yield, calculate the theoretical mass from the equation first, then percentage yield = (actual mass of product / theoretical mass of product) x 100. Give at least two reasons a yield is below 100 percent: the reaction is reversible and does not go to completion, product is lost on transfer or when filtering, or reactants react in unintended ways to give by-products.
- For atom economy, use atom economy = (Mr of the desired product / sum of the Mr of all products) x 100, taking the balancing numbers into account, and remember it is a property of the equation, so it does not change with the scale or the yield.
Worked example
In a titration, 25.0 cubic centimetres of sodium hydroxide solution is exactly neutralised by 20.0 cubic centimetres of 0.100 moles per cubic decimetre hydrochloric acid. NaOH + HCl gives NaCl + H2O. Calculate the concentration of the sodium hydroxide in moles per cubic decimetre.
- Convert the acid volume: 20.0 cubic centimetres = 20.0 / 1000 = 0.0200 cubic decimetres.
- Moles of HCl = concentration x volume = 0.100 x 0.0200 = 0.00200 mol.
- Use the mole ratio: NaOH reacts with HCl in a 1 to 1 ratio, so moles of NaOH = 0.00200 mol.
- Convert the alkali volume: 25.0 cubic centimetres = 0.0250 cubic decimetres.
- Concentration of NaOH = moles / volume = 0.00200 / 0.0250 = 0.0800 moles per cubic decimetre.
- Final answer: 0.0800 moles per cubic decimetre, which is 0.0800 x 40 = 3.2 grams per cubic decimetre if the question asks for mass concentration.
Practice questions
Try each question, then tap to reveal the answer.
Q1Convert 250 cubic centimetres into cubic decimetres.Show answer
Answer: 250 / 1000 = 0.25 cubic decimetres.
Q2Calculate the concentration in moles per cubic decimetre of a solution containing 0.5 mol in 250 cubic centimetres.Show answer
Answer: 0.5 / 0.25 = 2.0 moles per cubic decimetre.
Q3Convert a concentration of 0.20 moles per cubic decimetre of NaOH into grams per cubic decimetre. (Mr = 40)Show answer
Answer: 0.20 x 40 = 8.0 grams per cubic decimetre.
Q4Give the formula for percentage yield.Show answer
Answer: Percentage yield = (actual mass of product / maximum theoretical mass of product) x 100.
Q5State two reasons why a percentage yield is less than 100 percent.Show answer
Answer: Any two of: the reaction is reversible and does not go to completion, some product is lost during transfer or filtration, and side reactions produce unwanted by-products.
Q6Give the formula for atom economy.Show answer
Answer: Atom economy = (Mr of the desired product / sum of the Mr of all products) x 100.
Q7Why do companies prefer reactions with a high atom economy?Show answer
Answer: Less of the reactant mass ends up as waste, so raw materials are used efficiently, less waste must be treated or disposed of, and the process is cheaper and more sustainable.
Exam-style questions
Written in the style of a GCSE Science exam paper, with a full mark scheme.
A student makes copper sulfate crystals and obtains 6.4 g. The maximum theoretical mass is 8.0 g. Calculate the percentage yield and give two reasons why it is below 100 percent.
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Hydrogen can be made by reacting methane with steam: CH4 + H2O gives 3H2 + CO. Calculate the atom economy for the production of hydrogen. Relative formula masses: H2 = 2, CO = 28.
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This topic is chapter 21 of GCSE Chemistry Workbook, the whole course as one free printable PDF.
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