A theoretical yield calculator is a specialized tool designed to determine the maximum possible amount of product that can be formed in a chemical reaction under ideal conditions.
For example, consider the reaction between sodium hydroxide (NaOH) and hydrochloric acid (HCl):
NaOH + HCl → NaCl + H2OIf you start with 40g NaOH and excess HCl, the would determine that the maximum possible yield of NaCl would be 58.5g.
Theoretical Yield Calculator
| Reaction | Reactants | Theoretical Yield | Actual Yield | Percent Yield |
|---|---|---|---|---|
| 2H₂ + O₂ → 2H₂O | H₂: 8g, O₂: 32g | 36g H₂O | 33g H₂O | 91.7% |
| 2Na + Cl₂ → 2NaCl | Na: 46g, Cl₂: 71g | 117g NaCl | 108g NaCl | 92.3% |
| C₂H₅OH + 3O₂ → 2CO₂ + 3H₂O | C₂H₅OH: 46g, O₂: 96g | 88g CO₂ | 82g CO₂ | 93.2% |
| N₂ + 3H₂ → 2NH₃ | N₂: 28g, H₂: 6g | 34g NH₃ | 30g NH₃ | 88.2% |
| CaCO₃ → CaO + CO₂ | CaCO₃: 100g | 56g CaO | 50g CaO | 89.3% |
| C₆H₁₂ + O₂ → 6CO + 6H₂O | C₆H₁₂: 78g, O₂: 192g | 132g CO | 120g CO | 90.9% |
| Fe + CuSO₄ → FeSO₄ + Cu | Fe: 55.8g, CuSO₄: 159.6g | 63.5g FeSO₄ | 60g FeSO₄ | 94.0% |
| CH₄ + O₂ → CO + 2H₂O | CH₄: 16g, O₂: 32g | 18g CO | 15g CO | 83.3% |
| C₈H₁₈ + O₂ → CO₂ + H₂O | C₈H₁₈: 114g, O₂: 288g | 176g CO₂ | 170g CO₂ | 96.6% |
| PCl₃ + H₂O → HCl + H₃PO₃ | PCl₃: 137.33g, H₂O: 18g | 153.33g HCl | 140g HCl | 91.1% |
Theoretical Yield Formula
The theoretical yield can be calculated using the following formula:
Theoretical Yield = (Moles of limiting reagent × Stoichiometric coefficient of product) × Purity of productIn this formula:
- The moles of limiting reagent refers to the number of moles of the reactant that is present in the smallest amount compared to the other reactants.
- The stoichiometric coefficient of product refers to the number of moles of the product that is formed for every mole of the limiting reagent consumed in the reaction.
- The purity of product refers to the degree of purity of the product, which can range from 0 to 1.
For example, a reaction between sodium hydroxide (NaOH) and hydrochloric acid (HCl) to produce sodium chloride (NaCl) and water (H2O):
NaOH + HCl → NaCl + H2OAssume that we have 10 grams of NaOH and 15 grams of HCl, and we want to calculate the theoretical yield of NaCl.
First, we need to convert the masses of the reactants to moles:
- Moles of NaOH = 10 g / 40.0 g/mol = 0.25 mol
- Moles of HCl = 15 g / 36.5 g/mol = 0.411 mol
Since NaOH is the limiting reagent, we can use its moles to calculate the theoretical yield of NaCl:
Theoretical Yield of NaCl = (0.25 mol × 1) × 1.0 = 0.25 molNow, we can convert the moles of NaCl to grams:
Mass of NaCl = 0.25 mol × 58.4 g/mol = 14.6 gThe theoretical yield of NaCl in this reaction is 14.6 grams, assuming that the reaction goes to completion and there are no side reactions or losses during the process.
How to Calculate Theoretical Yield?
To calculate theoretical yield, follow these steps:
- Balance the chemical equation
- Identify the limiting reagent
- Calculate the moles of limiting reagent
- Use the stoichiometric ratio to determine product moles
- Convert moles to mass using molar mass
Using the reaction:
2Al + 3Cl2 → 2AlCl3With 54g Al and 213.5g Cl2:
- Convert to moles: Al = 2 moles, Cl2 = 3 moles
- Limiting reagent: Both reactants are in stoichiometric ratio
- Theoretical yield = (133.5 g/mol × 2 moles) = 267g AlCl3
Suppose you have a reaction between ethanol (C2H5OH) and oxygen (O2) to produce carbon dioxide (CO2) and water (H2O):
C2H5OH + 3O2 → 2CO2 + 3H2OIf you start with 10 grams of ethanol with a purity of 95%, what is the theoretical yield of carbon dioxide?
- The limiting reagent is ethanol (C2H5OH) since it’s present in smaller amounts compared to oxygen.
- The stoichiometric coefficient for carbon dioxide (CO2) is 2.
- The purity of ethanol is 95%.
Now, apply the theoretical yield formula:
- Moles of ethanol = 10 g / 46.07 g/mol = 0.217 mol
- Theoretical Yield of CO2 = (0.217 mol × 2) × 0.95 = 0.412 mol
Finally, convert moles of CO2 to grams:
Mass of CO2 = 0.412 mol × 44.01 g/mol = 18.1 gThe theoretical yield of carbon dioxide in this reaction is 18.1 grams, assuming that it goes to completion without side reactions or losses during processing.
Is Theoretical Yield Always 100%?
No, the theoretical yield is not always 100%. The theoretical yield can be less than 100% for several reasons:
- Purity of Reactants: If the reactants are not 100% pure, the theoretical yield will be reduced by the purity factor. For example, if a reactant is only 95% pure, the theoretical yield will be 95% of the maximum possible yield.
- Side Reactions: If any side reactions occur during the process, some reactants will be consumed in these side reactions, reducing the amount of product formed. This will lower the theoretical yield.
- Incomplete Reactions: If a reaction does not go to completion, the theoretical yield will be reduced. This can happen if the reaction is kinetically or thermodynamically unfavorable or if some reactants are lost during the process.
What is the Difference Between Theoretical Yield and Actual Yield?
The theoretical yield and the actual yield are two distinct concepts:
The key differences include:
- Theoretical yield is the calculated maximum yield
- Actual yield is the amount actually obtained
- Percent yield = (Actual yield/Theoretical yield) × 100
Theoretical Yield:
- The theoretical yield is the maximum amount of product that can be obtained from a chemical reaction or physical process, assuming completion without side reactions or losses.
- It is calculated based on stoichiometric relationships between reactants and products, as well as their purity.
- The theoretical yield represents an ideal scenario for any process.
Actual Yield:
- The actual yield is the amount of product that is actually obtained from a chemical reaction or physical process in a real-world setting.
- It accounts for various factors affecting processes such as side reactions, incomplete reactions, experimental losses, and practical limitations.
- The actual yield is typically lower than theoretical yield since achieving 100% efficiency is rare.
How to Calculate Theoretical Yield in Chemistry
To calculate the theoretical yield in chemistry, follow these steps:
Suppose you have a reaction between hydrogen gas (H₂) and oxygen gas (O₂) to produce water (H₂O):
2H₂ + O₂ → 2H₂OIf you start with 5 liters of hydrogen gas at 25°C and 1 atm pressure and 3 liters of oxygen gas at similar conditions, what is your theoretical yield of water (H₂O)?
The limiting reagent is oxygen (O₂), as it’s present in smaller amounts than hydrogen.
The stoichiometric coefficient for water (H₂O) is 2.
Assume purity of reactants and products is 100%.
First, convert gas volumes to moles:
- Moles of H₂ = (5 L × 1 atm) / (0.082057 L·atm/mol·K × 298.15 K) = 0.204 mol
- Moles of O₂ = (3 L × 1 atm) / (0.082057 L·atm/mol·K × 298.15 K) = 0.122 mol
Now apply your formula:
Theoretical Yield of H₂O = (0.122 mol × 2) × 1 = 0.244 molFinally, convert moles of H₂O to grams:
Mass of H₂O = 0.244 mol × 18.02 g/mol = 4.40 gYour theoretical yield of water (H₂O) in this reaction is 4.40 grams!
How to Calculate Theoretical Yield in Grams
Follow these simple steps:
With reaction between sodium hydroxide (NaOH) and hydrochloric acid (HCl) to produce sodium chloride (NaCl) and water (H2O):
NaOH + HCl → NaCl + H2O
Start with 10 grams of NaOH and 15 grams of HCl, what is the theoretical yield of NaCl in grams?
The limiting reagent is NaOH, as it is present in the smallest amount compared to HCl.
The stoichiometric coefficient of NaCl is 1.
The purity of both reactants and products is assumed to be 100%.
Converting Masses to Moles
- Moles of NaOH =
10 g / 40.0 g/mol = 0.25 mol- Moles of HCl =
15 g / 36.5 g/mol = 0.411 mol
Applying the Theoretical Yield Formula
Theoretical Yield of NaCl = (0.25 mol × 1) × 1.0 = 0.25 molConverting Moles to Grams
Mass of NaCl = 0.25 mol × 58.4 g/mol = 14.6 gThe theoretical yield of sodium chloride (NaCl) in this reaction is 14.6 grams.
How to Calculate Theoretical Yield from Limiting Reagent
To calculate the theoretical yield from the limiting reagent:
Consider a reaction between ethanol (C₂H₅OH) and oxygen (O₂) producing carbon dioxide (CO₂) and water (H₂O):
C₂H₅OH + 3O₂ → 2CO₂ + 3H₂OStart with 10 grams of ethanol and 20 grams of oxygen, what is the theoretical yield of carbon dioxide (CO₂)?
- The limiting reagent is ethanol (C₂H₅OH) since it is present in a smaller amount than oxygen.
- The stoichiometric coefficient for carbon dioxide (CO₂) is 2.
- The purity of both reactants and products is assumed to be 100%.
Converting Masses to Moles
- Moles of ethanol =
10 g / 46.07 g/mol = 0.217 mol- Moles of oxygen =
20 g / 32 g/mol = 0.625 mol
Since ethanol is our limiting reagent:
Theoretical Yield of CO₂ = (0.217 mol × 2) × 1.0 = 0.434 molConverting Moles to Grams
Mass of CO₂ = 0.434 mol × 44.01 g/mol = 19.1 gThe theoretical yield of carbon dioxide (CO₂) from this reaction is approximately 19.1 grams.
How to Calculate Percentage Yield from Mass
Suppose you are producing sodium chloride (NaCl) from the reaction between sodium hydroxide (NaOH) and hydrochloric acid (HCl):
NaOH + HCl → NaCl + H2OYou start with 10 grams of NaOH and 15 grams of HCl. The theoretical yield of NaCl can be calculated as follows:
Determine the Limiting Reagent: NaOH is the limiting reagent, as it is present in a smaller amount compared to HCl.
Convert Masses to Moles:
- Moles of NaOH = 10 g / 40.0 g/mol = 0.25 mol
- Moles of HCl = 15 g / 36.5 g/mol = 0.411 mol
Calculate the Theoretical Yield of NaCl:
Theoretical Yield of NaCl = (0.25 mol × 1) × 1.0 = 0.25 molMass of NaCl = 0.25 mol × 58.4 g/mol = 14.6 gLet’s say that in your experiment, you actually obtained 13.5 grams of NaCl.
To calculate the percentage yield:
Percentage Yield = (Actual Yield / Theoretical Yield) × 100%Percentage Yield = (13.5 g / 14.6 g) × 100% = 92.5%The percentage yield of NaCl in this reaction is 92.5%, indicating that the actual amount of product obtained is 92.5% of the theoretical maximum.
What is the Theoretical Yield of Aspirin?
The synthesis of aspirin typically involves the reaction between salicylic acid and acetic anhydride, with an acid catalyst like sulfuric acid (H2SO4) to produce aspirin and acetic acid:
C6H5COOH + (CH3CO)2O → C6H4(OCOCH3)COOH + CH3COOHWith 20 grams of salicylic acid (C6H5COOH) and 25 grams of acetic anhydride ((CH3CO)2O) available for synthesizing aspirin.
Convert masses to moles:
Moles of salicylic acid = 20 g / 138.12 g/mol = 0.145 molMoles of acetic anhydride = 25 g / 102.09 g/mol = 0.245 molThe limiting reagent here is salicylic acid since it’s present in a smaller amount.
Apply Theoretical Yield Formula: Theoretical Yield of Aspirin = (0.145 mol × 1) × 1.0 = 0.145 molFinally, convert moles to grams:
Mass of Aspirin = 0.145 mol × 180.16 g/mol = 26.1 gThe theoretical yield of aspirin in this reaction is 26.1 grams, assuming complete reaction with no side reactions or losses.
References
- Journal of Chemical Education – https://pubs.acs.org/journal/jceda8
- American Chemical Society – https://www.acs.org/education/resources
- Royal Society of Chemistry – https://www.rsc.org/education/teachers
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