Percent yield is the product actually obtained divided by the most the stoichiometry allows, and it is the first number to compute for any process. A tonne of salt can make at most 906 kg of soda ash, a kilogram of sulfur at most 3.06 kg of sulfuric acid, and a kilogram of hydrogen at most 5.67 kg of ammonia. Yields of successive steps multiply, so three good steps can still leave a poor total, and recycling unreacted material is what lifts a low per-pass conversion toward completion.
Part of Industrial Chemistry
The arithmetic of how much a reaction can make, how much it does make, and how recycling and multi-step losses change the total.
Three Different Numbers Often Called Yield
- Conversion: the fraction of a reactant that reacts in one pass.
- Selectivity: the fraction of what reacts that becomes the wanted product instead of by-products.
- Overall yield: actual product divided by the theoretical maximum from the starting reactant, including every loss.
Add a fourth, atom economy: wanted product mass divided by the total mass of reactants in the balanced equation. It tells you how much of what you feed becomes waste even at 100% yield.
The carrier supplies the reactions. The corpus pages that give practical recovery figures are named where they are used below; this article does not state a practical yield for any process without a source.
What You Need
- A balanced equation for each step.
- Atomic masses (rounded: H 1, C 12, N 14, O 16, Na 23, S 32, Cl 35.5, Ca 40).
- Weighed inputs and outputs from real runs.
- A notebook that records losses per step, not just the total.
Method: Computing A Yield
Step 1: Balance the equation and compute molar masses.
Step 2: Compute the theoretical output from the mass of the limiting reactant.
Step 3: Weigh the actual product (dry, at a stated purity).
Step 4: Divide. Record it.
Step 5: Repeat per step for multi-step processes and multiply.
Worked Example 1: Soda Ash From Salt (Solvay)
The overall reaction in the carrier is 2NaCl + CaCO3 → Na2CO3 + CaCl2.
- Molar masses: NaCl = 23 + 35.5 = 58.5, so 2 NaCl = 117. CaCO3 = 40 + 12 + 48 = 100. Na2CO3 = 46 + 12 + 48 = 106. CaCl2 = 40 + 71 = 111.
- Mass balance: 117 + 100 = 217 on the left, 106 + 111 = 217 on the right.
- Soda ash per kilogram of salt: 106 ÷ 117 = 0.906. So 1,000 kg of NaCl can give at most 906 kg of Na2CO3.
- If a run actually made 650 kg (an illustrative figure), the yield is 650 ÷ 906 = 72%.
- Atom economy: 106 ÷ 217 = 49%. More than half the reactant mass leaves as calcium chloride, which is why Waste Treatment must plan for it. See Solvay Chemistry.
Worked Example 2: Ammonia, And What Recycling Does
N2 + 3H2 → 2NH3. Hydrogen is 2 g per mole; ammonia 17 g per mole.
- 1 kg of hydrogen is 1,000 ÷ 2 = 500 mol.
- Ammonia formed: 500 × 2 ÷ 3 = 333 mol, which is 333 × 17 = 5,667 g, so 5.67 kg.
Per-pass conversion is low (the carrier says at atmospheric pressure the reaction barely produces ammonia, and it advises recycling unreacted gas through the catalyst bed). As an illustration, assume 15% of the feed reacts each pass and the product is removed each time. The unreacted fraction after n passes is 0.85ⁿ.
| Passes | Unreacted | Cumulative conversion |
|---|---|---|
| 1 | 0.85 | 15% |
| 5 | 0.85⁵ = 0.44 | 56% |
| 10 | 0.85¹⁰ = 0.20 | 80% |
| 20 | 0.85²⁰ = 0.04 | 96% |
Recycling lifts a 15% per-pass conversion to about 80% after ten passes. A purge to stop impurities building up always takes some gas out of the loop, so the true total is lower. The per-pass figure is illustrative, not a corpus or measured value. The hazard of the process, rather than its yield, is the subject of Haber Process.
Worked Example 3: Stage Yields Multiply
For sulfuric acid, 1 kg of sulfur (32 g per mole) becomes H2SO4 (98 g per mole): 98 ÷ 32 = 3.06 kg at 100% yield. From pyrite, Pyrite Roasting gives a recovery of 50-70% of the sulfur, about 250-370 g per kg of pyrite. Take 60% as a mid-point and, as illustrative values, 95% conversion of SO2 to SO3 and 98% absorption.
Overall = 0.60 × 0.95 × 0.98 = 0.559, about 56%. The weak step is the first one, so effort on the roaster pays more than on the absorber. At the page’s range, a kilogram of pyrite yields 0.25 × 3.06 = 0.77 kg to 0.37 × 3.06 = 1.13 kg of sulfuric acid at 100% yield of the later steps.
Common Mistakes
- Quoting a yield without saying what it is a fraction of.
- Weighing wet product.
- Ignoring the by-product mass.
- Treating conversion and yield as the same.
Safety
Chasing yield can push a process past its safe limits
Raising temperature, pressure or feed rate to gain a few per cent of yield can take a reactor outside the range its vessels and seals were tested for. Do not do it without redoing the pressure and heat checks in Pressure and Temperature and Heat Management.
What’s Next
- Learn next: Batch vs Continuous — where recycle loops live
- Combine with: Catalysts — raising conversion at moderate temperature