Theoretical Yield Formula: Definition, Method, Solved Example

Theoretical Yield Formula: The theoretical yield refers to the quantity of a product obtained when the limiting reactant in a chemical process is completely converted. It is crucial to note that the theoretical yield, which is measured in grams or moles, is distinct from the actual yield, which represents the product obtained in a real-world laboratory reaction. The actual yield may surpass the theoretical yield due to factors such as additional reactions producing more product or the presence of impurities in the recovered product.

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How to Determine Theoretical Yield

Understanding the expected product quantity based on given reactant quantities before initiating chemical reactions is essential, and this is where the concept of theoretical yield comes into play. It not only helps calculate the theoretical yield of a chemical process but also aids in determining the amount of each reagent required to produce a specific quantity of product.

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Calculating Theoretical Yield: A Sample Calculation

Let's illustrate how to calculate theoretical yield with an example:

Suppose you want to determine the total amount of water produced when 10 grams of hydrogen gas are burned in the presence of excess oxygen gas, following the chemical equation:

Step 1: Ensure that the chemical equation is balanced:

The initial equation is unbalanced but becomes balanced after the adjustment:

2H ₂ (g) + O ₂ (g) → 2H ₂ O (l)

Step 2: Calculate the mole ratios between reactants and products:

The mole ratio between chemicals is a crucial link between the reactant and the resulting product. In this case, the mole ratio between H ₂ and H ₂ O is 1 mol H ₂ to 1 mol H ₂ O.

Step 3: Calculate the theoretical yield of the reaction:

Use the following approach:

• Convert grams of the reactant to moles of the reactant using the reactant's molar mass.
• Convert moles of the reactant to moles of the product using the mole ratio between reactant and product.
• Finally, convert moles of the product to grams of the product using the molar mass of the product.

Applying this to the example:

The molar mass of H ₂ gas = 2 grams/mol

The molar mass of H ₂ O= 18 grams/mol

So, the theoretical yield of H ₂ O is calculated as follows:

grams H ₂ O = 10 g H2 x (1 mol H2 / 2 g H2) x (1 mol H ₂ O/ 1 mol H2) x (18 g H ₂ O / 1 mol H2O)

Simplifying the units:

grams H ₂ O= (10 x 1/2 x 1 x 18) g H2O

grams H ₂ O = 90 g H2O

Therefore, theoretically, 10 grams of hydrogen gas, when reacted with excess oxygen, will yield 90 grams of water.

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Theoretical Yield Formula Solved Example

Example: How do we calculate the theoretical yield of geranyl formate production when starting with 375 grams of geraniol, and the chemist obtains 417 grams of refined product with a quoted yield percentage of 94.1%?

Solution:

Actual yield = 417 g (the amount of the target product)

Percentage yield = 94.1%

To calculate the theoretical yield, you can use the following method:

Theoretical yield = (Actual yield / Percentage yield) x 100

= (417 / 94.1) x 100

= 443 g

In this case, the theoretical yield of geranyl formate is 443 grams.

Understanding Limiting Reactants and Percent Yield

To determine the theoretical yield, one must identify the limiting reactant in a balanced chemical equation. The limiting reactant is the reactant that is exhausted first and restricts the continuation of the reaction.

To find the limiting reactant

• Convert the given quantities of reactants to grams (if provided in moles).
• Divide the mass of each reactant by its molecular weight to obtain the number of moles.
• Compare the obtained moles with the balanced chemical equation's mole ratio to identify the limiting reactant.
• The percent yield is a valuable metric in chemical production. It quantifies the efficiency of a reaction by comparing the actual yield obtained in a laboratory setting with the theoretical yield calculated using stoichiometry.

Percent Yield = (Actual Yield / Theoretical Yield) x 100 percent

In industrial manufacturing, achieving a high percent yield is critical as it minimizes waste and maximizes product output. A low percent yield in any step of a multi-step production process can lead to substantial material and financial losses.