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# Theoretical Yield: All you need to know

Theoretical yield is the amount of substance that is formed in a chemical reaction.

#### Steps

1. Balance the chemical equation
2. Determine the mole ratio between the given reactant and product in question
3. Find the unknown using the formula

Moles = mass / molar mass

• Use mole ratio to find the unknown using the known

### Example 1

40.5 g of H2O2 is decomposed, (molar mass = 34.0 g/mol) according to the equation:

H2O2 –> H2O + O2 (unbalanced) Calculate number of moles of oxygen produced

STEP 1: BALANCE

H2O2 –> H2O + O2

The balanced equation will be as follows

2H2O2 –> 2H2O + O2

STEP 2: MOLE RATIO

We first find number of moles of H2O2 decomposed.

Moles = mass / molar mass

moles = 40.5 g / 34.0 g/mol

= 1.19 moles

Now, the mole ratio between 2H2O2 and O2 = 2 : 1

Thus, according to the equation, 2 moles of 2H2O2 forms 1 mole of O2.

STEP 3: THEORETICAL YIELD

How many moles of O2, will be formed from 1.19 moles of 2H2O2

2 = 1

1.19 =?

1.19 * 1 / 2 = 0.595 moles

Moles of oxygen = 0.595 moles

### Example 2

According to the equation 2H2 + O2 => 2H2O, 10.0 g of O2 is consumed if the reaction’s yield is 100%. Calculate mass of water in grams

First step, we check whether the equation is balanced.

According to the number of atoms on either side, the equation is balanced.

Second step, we calculate moles of Oxygen

Moles = mass / molar mass

= 10 / 32 = 0.3125 moles

Third step, find the mole ratio of oxygen to water.

Oxygen : Water

1 : 2

If 1 mole of oxygen would produce 2 moles of water when yield is 100% theoretically, what about 0.3125 moles ?

1 = 2

0.3125 = ?

0.3125 * 2 / 1

Moles of water = 0.625 moles

Molar mass of water is 18 g/mol

This means per 1 mole of water, there is 18 grams

We need to find mass of water in 0.625 moles

1 mole = 18 grams

0.625 moles = ?

0.625 * 18 / 1 = 11.25 grams

### Example 3

N2 reacts with H2 to produce NH3, calculate H2 moles that will produce 63.6 grams NH3 with excess N2.

N2(g) + 3H2(g)  2NH3(g).

This reaction will proceed until the available H2 is used up because N2 Is in excess

First, mole ratio of H2 to NH3

3 : 2

This means every 3 moles of H2 forms 2 moles of NH3

Number of moles in 63.6 grams of NH3 so that we can equate with this ratio

Moles of NH3 = mass / molar mass

moles = 63.6 / 17 = 3.74 moles

In our ratio, we have seen that ratio of H2 to NH3 is 3:2

H2 = NH3

3 : 2

? : 3.74

Moles of H2 = 3.74 moles * 3/2 = 5.61 moles of H2 is needed

Answer = 5.61 moles of H2

## Revision

What is yield?
The mass of a particular product formed in a reaction.

What is theoretical yield?
The maximum possible mass of product that could be formed in a reaction, calculated using the law of conservation of mass.

What three things do you need to know to calculate theoretical yield?
The mass of the limiting reactant, the relative formula masses of reactants and products, the balanced equation for the reaction.

What is a limiting reactant?
A reactant present in an amount less than that needed to react completely with the other reactant in a chemical reaction.

Amount of product actually obtained from reactions
Actual yield

Ratio of actual yield to theoretical yield expressed as a percent
Percent yield

Amount of product expected from chemical reaction
Theoretical yield

Reactant of which there is not enough
Limiting reactant

Reactant of which there is more than enough present for reaction
Excess reactant

Li made note cards to help him study for a test. The cards describe the steps required to calculate percent yield. However, Li dropped his note cards, so they are now out of order. Place the steps in the correct order by entering the numbers 1 through 5 next to the correct steps below.

Calculate the theoretical yield of the reaction.
Write a balanced chemical equation.
Check that all significant figures are correct in the calculated value.
Determine the limiting reactant in the reaction.
Divide the actual yield by the theoretical yield and multiply by 100.
3
1
5
2
4

Acetylene torches are used for welding, but the thermite reaction can be useful in situations in which acetylene torches are inappropriate, such as welding underwater. The thermite reaction is described by the equation below:

A welder has 1.873 × 102 g Fe2O3 and 94.51 g Al in his welding kit. Which reactant will he run out of first?

How much of this reactant should he order to make sure he runs out of both reactants at the same time? Round to the nearest hundredth and do not round any of your work until the very end.

He should order _ g of the limiting reactant.
Fe2O3
92.41g

Humans exhale carbon dioxide when they breathe. If the concentration of carbon dioxide in the air that people breathe gets too high, it can be fatal. Therefore, in space shuttles, submarines, and other sealed environments, it is common to use “air scrubbers” to remove carbon dioxide from the air. The air scrubbers on the space shuttle remove carbon dioxide by using lithium hydroxide (LiOH). The reaction in the air scrubbers is shown below:

CO2 + 2LiOH es001-1.jpg Li2CO3 + H2O

Each astronaut produces 8.8 × 102 g CO2 per day that must be removed from the air on the shuttle. If a typical shuttle mission is 9 days, and the shuttle can carry 3.50 × 104 g LiOH, what is the maximum number of people the shuttle can safely carry for one mission?
4

CO2 + 2LiOH mc001-1.jpg Li2CO3 + H2O

To ensure that the air in the shuttle remains free of excess CO2, engineers test the air-purification system. They combine

1.000 × 103 g LiOH with 8.80 × 102 g CO2.

The reaction produces 3.25 × 102 g H2O.

What is the limiting reactant in this test reaction?

What is the theoretical yield of this test reaction? Record answer to the nearest whole number.

What is the percent yield of the purification system reaction? Record answer to the tenths place.
CO2

360 g H2O

90.3

The electrolysis of water forms H2 and O2.

2H2O mc017-1.jpg 2H2 + O2

What is the percent yield of O2 if 10.2 g of O2 is produced from the decomposition of 17.0 g of H2O?
67.6%

Consider the balanced equation.

CuSO4 + Zn mc016-1.jpg ZnSO4 + Cu

If 200.0 g of copper(II) sulfate react with an excess of zinc metal, what is the theoretical yield of copper?
79.63 g

Consider the balanced equation.

2HCl + Mg mc031-1.jpg MgCl2 + H2

If 40.0 g of HCl react with an excess of magnesium metal, what is the theoretical yield of hydrogen?
1.11 g

The chemical equation shows iron(III) phosphate reacting with sodium sulfate.

2FePO4 + 3Na2SO4 mc010-1.jpg Fe2(SO4)3 + 2Na3PO4

What is the theoretical yield of Fe2(SO4)3 if 20.00 g of FePO4 reacts with an excess of Na2SO4?
26.52 g

Salicylic acid (C7H6O3) reacts with acetic anhydride (C4H6O3) to form acetylsalicylic acid (C9H8O4).

2C7H6O3(aq) + C4H6O3(aq) mc002-1.jpg 2C9H8O4(aq) + H2O(l)

What is the limiting reactant if 70.0 g of C7H6O3 and 80.0 g of C4H6O3 react?g
salicylic acid

Consider the combustion reaction for acetylene.

2C2H2(l) + 5O2(g) mc001-1.jpg 4CO2(g) + 2H2O(g)

If the acetylene tank contains 37.0 mol of C2H2 and the oxygen tank contains 81.0 mol of O2, what is the limiting reactant for this reaction?
O2

Ammonia is produced by the following reaction.

3H2(g) + N2(g) mc005-1.jpg 2NH3(g)

When 7.00 g of hydrogen react with 70.0 g of nitrogen, hydrogen is considered the limiting reactant because
7.5 mol of hydrogen would be needed to consume the available nitrogen.

Which statement correctly describes the relationship between reactant and yield?
The theoretical yield is calculated from the amount of the limiting reactant present.

A 13.00 g sample of citric acid reacts with an excess of baking soda as shown in the equation.

mc011-1.jpg

What is the theoretical yield of carbon dioxide?
8.93 g

Consider the balanced equation.

N2 + 3H2 mc033-1.jpg 2NH3

What is the percent yield of NH3 if the reaction of 26.3 g of H2 produces 79.0 g of NH3?
53.4%

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