# Question #e6e7e

Oct 31, 2017

Worked Example for calculating theoretical yield, actual yield, percent yield, and limiting reagent

#### Explanation:

Hi Kirby,

I can give you a worked example for one of your experiments and hopefully that will help you to complete the others?

1) Write a balanced equation of your reaction.

The experiment you carried out is the reaction that forms calcium carbonate, which has the following equation:

CaCl2 + Na2CO3 ------> CaCO3 + 2NaCl

2) Calculate the molecular weight (MW) of each component in your reaction.

The atomic weight (AW) of each element can be found on the periodic table:
Ca = 40.078 gmol-1; Cl = 35.45 gmol-1; Na = 22.990 gmol-1; C = 12.011 gmol-1; O = 15.999 gmol-1

To calculate the MW, you add together the AWs of all the elements in a compound:
CaCl2 MW = (2 x 35.45) + 40.078 = 110.98 gmol-1
Na2CO3 MW = (2 x 22.99) + (3 x 15.999) + 12.011 = 105.988 gmol-1
CaCO3 MW = 40.078 + 12.011 + (3 x 15.99) = 100.059 gmol-1
NaCl MW = 22.99 + 35.45 = 58.44 gmol-1

3) Convert mL of reactant to moles

You can do this using the equation n = CV; where n = number of moles, C = concentration, and V = volume.

For Sodium Carbonate C = 0.5 M or mol/dm3, and V = 10 mL or cm3. We need to convert cm3 into dm3 so that it is a balanced equation. 1000 cm3 = 1 dm3 so you divide 10 cm3 by 1000.

Number of moles = 0.5 mol/dm3 x (10cm3/1000) = 0.005 moles

For Calcium Chloride C = 2 mol/dm3 and V = 20 cm3 and again you need to convert the volume by dividing by 1000.

Number of moles = 2 mol/dm3 x (20cm3/1000) = 0.04 moles

From this calculation we have determined what the limiting reagent is – it is the reagent of which you use the least number of moles.

It is called the limiting reagent because it limits how far the reaction can go e.g. if you only have a certain number of moles of sodium carbonate, you can only form a certain amount of calcium carbonate (you won’t have enough CO3 to form anymore).

In this experiment, you have 0.005 moles of sodium carbonate and 0.04 moles of calcium chloride – thus sodium carbonate is the limiting reagent.

4) Determine theoretical yield.

Now that you have calculated the number of moles of reagent used, and have the limiting reagent, you can calculate the theoretical yield. The theoretical yield is the yield that would be produced if you had 100% conversion from your reagents to your products.

Going back to your balanced equation from step 1 – the limiting reagent (Na2CO3) is in a 1:1 ratio with your product (CaCO3).

i.e. Moles limiting reagent = Moles product

Thus, the theoretical yield is 0.005 moles of calcium carbonate.

You can convert this into grams using the MW we calculated in part 2 for calcium carbonate, and the following equation:
Mass (g) = No. Moles x MW
Mass (g) = 0.005 mol x 100.059 gmol-1 = 0.5 g

5) Determine Actual Yield and Percentage Yield

Your actual yield is the amount of product (in g) that you actually produced. You can calculate this by finding the difference between the start and end weight of your evaporating dish and filter paper (the difference will be equal to the weight of product produced).

Actual yield = 39.6040 g – (39.1780 g + 0.3888 g) = 0.372 g

Then your percentage yield is the percentage of your theoretical yield that you actually produced

i.e. Actual Yield/Theoretical Yield x 100

0.372/0.5 x 100 = 74.4%

A good yield!

Let me know if you have any further questions.