Theoretical Yield Calculator – Calculate Theoretical Yield in Chemical Reactions

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 + H2O

If 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 product

In 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 + H2O

Assume 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 mol

Now, we can convert the moles of NaCl to grams:

Mass of NaCl = 0.25 mol × 58.4 g/mol = 14.6 g

The 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 → 2AlCl3

With 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 + 3H2O

If 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 g

The 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 → 2H₂O

If 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 mol

Finally, convert moles of H₂O to grams:

Mass of H₂O = 0.244 mol × 18.02 g/mol = 4.40 g

Your 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 mol

Converting Moles to Grams

Mass of NaCl = 0.25 mol × 58.4 g/mol = 14.6 g

The 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 + 3H₂O

Start 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 mol

Converting Moles to Grams

Mass of CO₂ = 0.434 mol × 44.01 g/mol = 19.1 g

The 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 + H2O

You 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 mol

Mass of NaCl = 0.25 mol × 58.4 g/mol = 14.6 g

Let’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 + CH3COOH

With 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 mol

Moles of acetic anhydride = 25 g / 102.09 g/mol = 0.245 mol

The 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 mol

Finally, convert moles to grams:

Mass of Aspirin = 0.145 mol × 180.16 g/mol = 26.1 g

The 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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