# Stoichiometry - a review

## Skills tested by this Quiz

• evaluate molecular weight for a given formula
• evaluate weight (mass) percentages of elements for a given formula
• evaluate amounts (in mass and mole units) produced in a chemical reaction from given conditions
• classify reactions by types: combination, combustion, displacement, formation, etc
• determine the chemical formula when weight percentages are given and then evaluate the mole percentages of elements in the formula
• determine the chemical formula when weight percentages are given and molecular weight is known
• determine the amount produced, the actual yield, and other stoichiometry quantities for a given reaction

## Stoichiometry Review

### Review Purposes

• To get an overall view of stoichiometry.
• Apply skills learned to perform quantitative chemical analysis.
• Apply theories and rules of chemistry to solve problems.
• Assess areas of strength and weakness for review purposes.
• Improve problem solving strategy and learning efficiency.

## Stoichiometry

STOICHIOMETRY is the quantitative relationship of reactants and products. This unit has been divided into the following objects. A brief review is given here so that you can get a birds'-eye or overall view of stoichiometry.
1. Amounts of substances
Express amounts of substance in mass units of g, kg, tons, and convert them to moles, kilomoles, or millimoles.
2. Chemical formulas
Represent a substance with a formula that reflects its chemical composition, structure, and bonding; evaluate weight and mole percentages of elements in a substance; and determine chemical formula by elemental analysis.
3. Reaction features
Define some common features of chemical reactions; classify chemical reactions by common features such as combination, combustion, decomposition, displacement, and redox reactions.
4. Reaction equations
Express quantitative relationship using chemical reaction equations; evaluate quantities of reactants and products in a chemical reaction; and solve reaction stoichiometry problems.
5. Excess and limiting reagents
Define excess and limiting reagents; determine excess and limiting reagents in a reaction mixture; and determine quantities produced in a chemical reaction.
6. Yields
Define theoretical and actual yields due to limiting reagent; apply the concept of limiting reagent to evaluate theoretical yield; convert actual yield to percentage yields.

## A Typical Quiz

In these quizzes, we give a set of question that are inter related.

Problem 1

You have weighed x g of CaCl2 (molar mass 111) for an experiment dealing with chloride ions and you need to find the number of moles of Cl- ions. Show the conversion from x g CaCl2 to moles of Cl- ions.

Hint...
The conversion logic in given below:

```          1 mol CaCl2   2 mol Cl-      2 x
x g CaCl2 -----------  ----------- = ------ mol Cl-
111 g CaCl2  1 mol CaCl2     111
```

Skill...
Convert amounts of substances in various units.

Problem 2

You have a sample weighing 2.345 g containing equal weight of CaCl2 (f.wt. 111) and AlCl3 (f.wt. 133). How many mole of Cl- ions do you have?

Hint...
Assume you understand the previous Example, then you can give

```   2 mol     3 mol     2.345 g
( -----  +  ----- ) x ------- = 0.04757 mol Cl-.
111 g     133 g       2
```

Skill...
Develop skills to calculate moles of chloride ions in problems containing unequal weights of CaCl2 and AlCl3.

Problem 3

When a 2.00-g mixture of CaCl2 (111) and RbCl (121) was analyzed, the result reports that the mixture contains a total of 0.0241 mol Cl- ions. Find weight percentage of RbCl in the sample.

Hint...
Using the method in the previous examples, and assume x g RbCl are present in the mixture, you have

```   x     2 (2.00-x)
----- + -----------  =  0.0241
121      111```

Solving for x, x = 1.23 g (Practice your solution)

Percentage = 1.23 / 2.00 = 61.4 % RbCl.

Skill...
Making an assumption to make the problem solvable.

Problem 4

When a 2.00-g mixture of CaCl2 (111) and RbCl (121) was received by an analytical laboratory, the technician dissolved it in a solution and then he used excess amount of AgNO3 to precipitate the chloride as AgCl. He collected 3.456 g AgCl. What is the percentage of RbCl in the sample?

Hint...
We should convert 3.456 g AgCl into moles of AgCl or Cl- ions.

```             1 mol AgCl
3.456 g AgCl ------------ = 0.0241 mol AgCl or Cl-
143.4 g AgCl
```
The rest of the solution has already been given in Problem 3.

Skill...
Building skills to do useful work.

Problem 5

You are interviewed for a manager's job, and you were asked what you should instruct your technician to do for the following situation. Company X has received a sample containing a mixture of CaCl2 and BaCl2. The client of Company X needs to know the percentages of the two components.

Hint...
Instruct your technician to find out if the sample contains any other substance than CaCl2 and BaCl2

If it does not contain other substance than Ca2+, Ba2+, and Cl- ions, instruct him to precipitate the chloride ions with an excess amount of silver ion.

Instruct the technician how to calculate the moles of chloride present, and how to calculate the percentages.

Skill...
Write instructions for laboratory process.

## Example Problems

1. When properly used, urea, CH4N2O, is a good candidate for fertilizer. Unocal is one of the company that produces urea in Kenai, Alaska. It produces 1.1 million tons of urea each year. How many moles is this amount?

Urea is also called carbamide or carbonyldiamide. Since this is a US factory, 1 ton is taken as 983 kg that is equivalent to 18 thousand moles.

Skill -
Converting from mass units to moles and vice versa.

2. Urea is made by reacting carbon dioxide (CO2) with anhydrous ammonia (NH3) under 3,000 psi (pounds per square inch) pressure and at 350°F (177°C or 450 K). CO2 + 2 NH3 = CO(NH2)2 + H2O
. 44 . . . . 34 . . = . 60 . . . . . . . . 18 (molar mass)
The removal of water that occurs during the reaction is referred to as "dehydration." The resulting molten mixture is further processed into either prills or granules. For each ton of urea made, how much water is removed?

For 1.3 tons of reactants, 1.0 ton of urea is produced. By the way, 3,000 psi is equivalent to 200 atmosphere pressure.

Skill -
Interpret stoichiometry among products and reactants.

3. The NPK numbers (for example, 25, 3, 7) used in the fertilizer industry refers to the percentage of nitrogen, N, phosphorus, P, and potassium, K. What are the NPK numbers for pure urea?

Based on the formula, urea contains 46.7% N. However, the factory usually gives 46 because most products contain water.

Skill -
Calculate weight and mole percentage from chemical formula.

4. Conversion of nitrogen into protein by plants is a complicated process. First, urea is hydrolyzed and converted to ammonium carbonate. The hydrolysis of urea is brought about by the unease enzyme, but the reaction may be written as follows: CO(NH2)2 + 2 H2O = (NH4)2CO3
The product is a salt. The solubility of urea is reported to be 1 g in 1 ml of water. Assume that this solution is allowed to hydrolyze by the unease enzyme, which is the limiting reagent, urea or water?

One g of urea is 17 millimoles, which requires 34 millimoles of water to react from the stoichiometry of the reaction equation. One g of water is 56 millimole, that is more than 34 millimoles.

Skill -
Determine excess and limiting reagent.

5. Alanine CH3CH(NH2)(COOH) is one of the aminoacids that are the building blocks of proteins. What is the percentage of nitrogen in this aminoacid?

Skill -
Determine an element percentage from chemical formula.

6. An old method for protein analysis was to measure the nitrogen content. The amount of protein present was assumed to be 16 times the amount of nitrogen.

Assume that 50 % of the nitrogen in urea is converted to protein by plants. How much protein is produced for one gram of urea?

Percentages of protein in plant material are usually very low.

Skill -
Calculate theoretical yield, actual yield, and percentage yield.

7. A solid mixture containing Na2SO4 and NaCl. What compound would you use to precipitate the Cl- ion?

Skill -
Apply what you know of substances. AgCl is one of the insoluble few chloride.

8. A solid mixture containing Na2SO4 and NaCl. What compound would you use to precipitate the SO42- ion?

BaCl2 is a soluble salt, but BaSO4 is not.

Skill -
Apply what you know of substances.

9. A 2.21 g mixture containing Na2SO4 and NaCl dissolved in water is treated with BaCl2. The resulting dry BaSO4 weighs 2.57 g. How many mole(s) of BaSO4 was collected? (formula wt. BaSO4, 233.39)

2.57 g / (233.39 g/mol) = ? mol

How many mole(s) of Na2SO4 was present in the mixture? (Also 0.0110 mol)

Skill -
Performing unit conversion tasks.

10. A 2.21 g mixture containing Na2SO4 and NaCl dissolved in water is treated with BaCl2, and analysis shows 0.01101 mol Na2SO4 was present. What is the weight of Na2SO4? (formula wt. Na2SO4, 142.04)

Skill -
Performing unit conversion tasks.

11. A 2.21 g mixture containing 1.56 g Na2SO4 and some unknown impurities is treated with BaCl2. How many grams of BaSO4 should form? (formula wt. Na2SO4, 142.04, BaSO4, 233.39)

Conversion calculation:

```             233.39 g/mol BaSO4
1.56 g NaSO4 ------------------- = ? g BaSO4
142.04 g/mol Na2SO4
```

Skill -

You have acquired all the skills to perform chemical analysis to find out the percentage of certain component in a mixture. For example, consider this problem.

A 2.21 g mixture containing Na2SO4 and NaCl dissolved in water is treated with BaCl2, and 2.57 g of BaSO4 was obtained. What is the percentage of NaCl in the sample?

12. Which one of the following samples has the highest percentage of chloride?
1. pure CaCl2
2. pure AlCl3
3. equal weight mixture of CaCl2 and AlCl3
4. pure NaCl
5. pure BaCl2

Skill -
Interpret chemical formula

13. The reaction
C3H8 + 5 O2 = 3 CO2 + 4 H2O
is best classified as a
1. formation reaction
2. decomposition reaction
3. combustion reaction
4. exchange reaction
5. displacement reaction

Skill -
Describe the major features of chemical reactions.

14. What chemical (give the formula) would you use in order to determine the percentage of CaCl2 in a solid mixture of CaCl2 and Ca(NO3)2. Assume you can first dissolve the solid in water.

Skill -
Apply the rule: salts of nitrates are usually soluble.

15. A 1.140 g mixture of NaCl and CaCl2 dissolved in water is mixed with sufficient solution of AgNO3 to give 2.868 g of dry AgCl. Calculate the WEIGHT percentage of NaCl? (Na, 23.0; Cl, 35.5; Ca, 40; Ag, 107.9)

Skill -
Technique suggestion:

2.868 g AgCl = 0.0200 mol (Cl- or AgCl)

Assume the mixture contains x g NaCl, then (1.140-x) g is CaCl2. Thus, we have:

# mol NaCl + 2 # mol CaCl2 = # mol Cl- lead to
```   x g NaCl         2 (1.140 - x) CaCl2
--------------  +  --------------------  = 0.0200 mol
58.5 g /mol          111.1 g/mol```

Solve the equation for x (x = 0.585 g) and calculate the percentage.

16. A 1.140 g mixture of NaCl and CaCl2 dissolved in water is mixed with sufficient solution of AgNO3 to give 2.868 g of dry AgCl. Calculate the MOLE percentage of NaCl? (Na, 23.0; Cl, 35.5; Ca, 40; Ag, 107.9)

Skill -
Determine the weight and mole percentages of mixtures.

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