How to use limiting reactant to determine theoretical yield
Since the limiting reactant is completely used up first during a reaction, it follows that the limiting reactant determines how much of the product you can possibly make. The amount of product you can possibly make based on the amount of the limiting reactant is called the theoretical yield.
To calculate theoretical yield, you must consider the following:
- If you know the mass of the limiting reactant, you must first use the molar mass of the reactant to convert from mass of reactant to moles of reactant. If you know the moles of the reactant, like we do from finding the limiting reactant, you should proceed directly to step 2.
- Use the mole-mole ratio between the limiting reactant and the product in the balanced chemical equation to convert the moles you got in step 1 to the corresponding moles of the product
- Multiply the moles of product from step 2 by its corresponding molar mass to get the theoretical yield
The above steps are summarized in the following diagram:
Now let’s solve the following problem
Question 1
Methane reacts with oxygen to produce carbon dioxide and water according to the following balanced chemical equation:
CH4+ 2O2 ———> CO2+ 2H2O
If 8.0 g of CH4 is the limiting reactant calculate the theoretical yield of CO2 and H2O.
Strategy
Continuing from question 1
Since we determined the moles of CH4 in question 1, it follows that we must use these moles and the mole-mole ratio from the balanced chemical equation to calculate the corresponding moles of CO2 and H2O that will react with it.
If we refer to the balanced chemical equation:
1 mol CH4 + 2 mol O2 ———> 1 mol CO2 + 2 mol H2O
You will notice that: 1 mol CH4= 1 mol CO2
It follows that the conversion factors from this relationship are:
1 mol CH4/1 mol CO2 and 1 mol CO2/1mol CH4
Therefore, to convert 0.498 mol CH4 to mol of CO2,
we will do: 0.489 mol CH4 x 1 mol CO2/1 mol CH4= 0.498 mol CO2
Since we now know the corresponding moles of CO2 to be 0.498 mol CO2, we will multiply this value by the molar mass of CO2. If we do, we will get:
0.498 mol CO2 x 44.01 g/mol CO2 = 21.9 g CO2, thus, the theoretical yield of CO2 is 21.9 g.
Similarly, for H2O, the mole-mole ratio between H2O and CH4 is:
1 mol CH4= 2 mol H2O. The corresponding conversion factors are: 1 mol CH4/2 mol H2O and
2 mol H2O/1 mol CH4
Therefore, to covert 0.498 mol CH4 to mol H2O, we will do:
0.489 mol CH4x 2 mol H2O/1 mol CH4= 0.978 mol H2O
Since we now know the corresponding moles of H2O to be 0.978 mol H2O, we will then multiply this value by the molar mass of H2O. If we do, we will get:
0.978 mol H2O x 18.01 g/molH2O = 17.6 g H2O, thus, the theoretical yield of H2O is 17.6 g.
How to calculate percentage yield
To calculate percentage yield, you must divide the actual yield by the theoretical yield, and then multiply the result by 100%. Mathematically, we can express this relationship as:
percentage yield = actual yield/theoretical x 100%
Why calculate percentage yield?
We calculate percentage yield to determine how much of the product is actually produced as a result of the reaction. As you may have thought, rarely do reactions produce 100% of the theoretical yield. This is because;
- unwanted side reactions may have occurred during the reaction
- separating the desired products from the reaction mixture may have been difficult
Now, imagine that if 10.00 g of CO2 was actually produced as a result of equation (1) above, calculate the percentage yield of CO2
Strategy
To calculate percentage yield, we will take the actual yield of CO2 divided by the theoretical yield, and then multiply the result by 100%. If we do, we will get:
10.00 g CO2/21.9 g CO2 x 100 % = 45.7%, thus, 45.7% CO2 was produced as a result of the reaction.
To determine limiting reactant, click here