Dimensional Analysis and Stoichiometry

Chapter 3: Stoichiometry (Chemical Formulas and Equations)

What is Stoichiometry?

Stoichiometry is the quantitative relation between number of moles (and mass) of the different reactants and products in a chemical reaction.

Chemical Formulas

A chemical formula is a notation used in science that shows the number and type of atoms present in a specific molecule. Chemical formulas can also be used to determine the molecular weight of a compound and percentage by mass of each element in a compound.

Multiple Choice

NaHCO₃ represents

• Sodium bicarbonate

• Sodium carbonate

• Sodium Chloride

• Calcium Carbonate

Multiple Choice

What is the total number of oxygen atoms in Ca₃(PO₄)₂?

• 2

• 4

• 6

• 8

• 40

Molecular Weight

The molecular or formula weight is the sum of the atomic weights of each atom in compound. The atomic weights for each element can be found on your periodic table.

Ex: H₂O has a molar mass of

2(1.0079 g/mol) + 15.9994 g/mol = 18.01528 g/mol

*Note: there are TWO hydrogen atoms, so you must multiply the atomic mass of hydrogen by 2

Multiple Choice

Calculate the molar mass of Cu₂O.

• 37 g/mol

• 45 g/mol

• 79.5 g/mol

• 143 g/mol

Multiple Choice

Calculate the molar mass of KOH.

• 28 g/mol

• 56 g/mol

• 84 g/mol

• 112 g/mol

Percentage Composition by Mass

This is found by dividing the mass of a component, or element, in a compound, by the entire compound's molar mass and multiplying that number by 100%.

Multiple Choice

What is the percent by mass of sodium in NaCl?

• 39%
• 61%
• 35%
• 65%

Multiple Choice

What is the percent by mass of oxygen in MgO?

• 20%
• 40%
• 50%
• 60%

Empirical Formulas

An empirical formula tells us the relative ratios of different atoms in a compound. So, a chemical formula will always be some integer multiple of the empirical formula. If you know the mass percentages of each element in a compound, you can...

1. Calculate the grams of each element
2. Calculate the moles of each element
3. Assign the empirical formula

Multiple Choice

You are given the following percentages: 40.05% S and 59.95% O. Find the empirical formula for these elements.

• SO

• SO2

• SO3

• SO4

Multiple Choice

Which pair has the same empirical formula?

• NaCrO₄ and Na₂Cr₂O₇
• C₂H₄O₂ and C₆H₁₂O₆
• C₃H₆O₃ and C₂H₆O₂
• CH₄ and C₂H₆

Chemical Reactions

• Chemical reactions involve the conversion of one or more substances, into one or more different substances- they result in chemical changes rather than physical changes

• During a chemical reaction, the distribution of atoms changes, but the number of atoms of each element does not change

• The Law of Conservation of Mass says that "atoms are neither created, nor destroyed, in any chemical reaction

• Ex: hydrogen gas (H₂) can react with oxygen gas (O₂) to create water (H₂O)

Multiple Choice

Provides evidence that a chemical reaction has occurred. 

• dissolving 
• melting
• formation of a gas
• bending

Multiple Choice

If you start a chemical reaction with 5 atoms of helium, how many atoms will you have after?

• 4 atoms
• 10 atoms
• 1 atom
• 5 atoms

Chemical Equations

• Chemical equations give the identities and quantities of substances involved in a reaction

• Chemical formulas that indicate the reactants, or what the reaction started with, are written on the left side of the equation, and products are written on the right side

• The arrow in the middle of the equation is read as "yields" or "reacts to form"

• When writing chemical equations, it is important to also include the states of matter

• Ex: 2H₂(g) + O₂(g) --> 2H₂O(l)

Balancing Chemical Equations

It is important to always make sure chemical equations are balanced, meaning the number of atoms for each element is equal on both sides. To do so, follow these steps:

Identify the most complex substance Adjust the coefficients Balance polyatomic ions as a unit Balance the remaining atoms Check your work

*You can ONLY adjust coefficients, NOT subscripts

Multiple Choice

Which of the following chemical equations is balanced?

• 3Na + Cl₂ --> 3NaCl
• 3AgBr + GaPO_{4 -->} Ag₃PO₄ + GaBr₃
• CO₂ + H₂O -->  C₆H₁₂O₆ + O₂
• 2H₂O + O₂ --> 2H₂O + OH

Multiple Choice

What is the correct balanced equation for the combustion of glucose (C₆H₁₂O₆)?

• C₆H₁₂O₆(s) + O₂(g) --> CO₂(g) + H₂O(l)

• C₆H₁₂O₆(s) + 6O₂(g) --> 6CO₂(g) + H₂O(l)

• C₆H₁₂O₆(s) + 6O₂(g) --> 6CO₂(g) + 6H₂O(l)

• C₆H₁₂O₆(s) + 3O₂(g) --> 3CO₂(g) + 3H₂O(l)

What does a balanced chemical equation help me determine?

A balanced chemical equation gives you a mole ratio, which can then be used to convert between masses of reactants and products.

Multiple Choice

Using the balanced equation below,
 CaC₂(s)   +  2H₂O(l)   -->   C₂H₂(g)   +   Ca(OH)₂(aq)
how many grams of Ca(OH)₂ would be formed with 3.20 moles of CaC₂?

• 119 g
• 21.2 g
• 114 g
• 237 g

Multiple Choice

Using the balanced equation below,
Mg(s)   +  2HCl(aq)  -->   MgCl₂(aq)   + H₂(g)
How many moles of HCl are consumed in the production of 7.5 moles of MgCl₂?

• 3.8 moles
• 15 moles
• 7.5 moles
• 23 moles

Different Types of Chemical Reactions

• Combination/Synthesis- two or more compounds combine to form one, more complex, compound (A + B --> C)

• Decomposition- one substance is broken down into two or more simpler products (A --> B + C)

• Single Displacement- a pure element switches place with another element in a compound (A + BC --> AC + B)

• Double Displacement- cations of two reactants switch places to form entirely new products (AB + CD --> AD + CB)

• Combustion- produce flames and releases heat, typically involves O₂(g) as a reactant and usually yields CO₂(g) and H₂O(l)

• Neutralization- reaction between an acid and a base, water is one of the products

Multiple Choice

Which type of reaction takes place in the presence of oxygen and produces carbon dioxide and water?

• double replacement 
• decomposition 
• combustion 
• single replacement

Multiple Choice

A student mixes two solutions, planning to produce carbon dioxide. Which of the following is the BEST evidence that a chemical reaction is producing carbon dioxide?

• color change
• formation of a solid
• temperature change
• formation of bubbles

How Do I know if a Single Displacement reaction will occur (based on the chemical equation)?

To determine this, you must use the Table J in your reference table. For a single displacement reaction to occur, the element that is doing the replacing, must be more reactive than the element in the compound.

In the example, A + BC --> AC + B, element A must be more reactive (higher up on the table) than element B

Multiple Choice

Based on the activity series, will this reaction occur?

Au (s) + HCl (aq) →

• Yes

• No

Multiple Choice

Based on the activity series, will this reaction occur?

Sr (s) + HCl (aq) →

• Yes

• No

Multiple Choice

Based on the activity series, which metal could X represent in the reaction below?

X + Ca (NO₃)₂ --> Ca + X (NO₃)₂

• Ba

• Fe

• Mg

• Zn

How do I know if a double displacement reaction will occur (based on the chemical equation)?

Double displacement reactions occur when they form an insoluble gas or an insoluble solid. You can determine if a compound will be soluble or insoluble from Table F in your reference table.

Multiple Choice

Which of the following compounds will not disassociate in water? 

• NaCl
• PbCl₂
• MgNO₃
• Na₂SO₄

Multiple Choice

Determine the two products when Na₃PO₄ reacts with SnO₂.

• NaO and SnPO₄

• Na₂O and Sn(PO₄)₂

• Na₂O and Sn₃PO₄

• Na₂O and Sn₃(PO₄)₄

Multiple Choice

Which is the name of the kind of solid substance formed in this figure?  

• aqueous 
• precipitate
• acid
• synthesis 

What are Limiting Reactants?

A limiting reactant is the reactant that is consumed first and limits the amount of product that can be formed. Any quantity of a reactant that is left over, is referred to as excess.

Analogy: In order to make 1 grilled cheese sandwich, you need 1 slice of cheese, and 2 slices of bread. Say you have 10 slices of bread and 4 slices of cheese. You can only make 4 sandwiches before you run out of cheese. Therefore, cheese is your limiting reactant, and you will have an excess of 2 slices of bread.

Multiple Choice

What is the limiting reactant if 10 moles of NH₃  react  with 30.0 moles of NO?
4NH₃+6NO --> 5N₂ + 6H₂O

• NH₃
• NO
• N₂
• water

Theoretical Yield vs. Actual Yield

Theoretical Yields are determined through calculations using the limiting reactant. Actual Yields are the amount of product actually produced. These two values can be used to determine percent yield, which is the ratio of actual yield to theoretical yield.

% Yield= (actual yield (g)/theoretical yield (g)) x 100%

Multiple Choice

CH₄  +  2O₂  →  CO₂  +  2H₂O
24 grams of CH₄ was added to the above reaction. Calculate the theoretical yield of CO₂.

• 66 grams
• 132 grams
• 33 grams
• 8.72

Multiple Choice

For the reaction represented by the equation Cl₂ + 2KBr → Br₂ + 2KCl, how many grams of potassium chloride can be produced from 356 grams potassium bromide?

• 749 g
• 225 g
• 479 g
• 814 g

Multiple Choice

When reacting Na with Cl₂, we calculated that the theoretical yield should be 13 grams. Our actual yield was 12.5 grams. What is the percent yield?

• 90.4%

• 104%

• 96.15%

• 1.04%

Multiple Choice

The ______________ yield is the maximum amount of product possible in a reaction. This determines the amount of product that should be produced in a perfect setting

• Percent
• actual
• stoichiometry
• theoretical

A Glimpse into Chapter 4

Let's use what we already know about balanced chemical equations and neutralization reactions, to solve a titration problem.

Say we want to find the molarity of an unknown acid..

We will use these steps:

1. Write a balanced equation for the neutralization reaction
2. Use the molarity of your known base, and the volume of your known base to calculate the number of moles of the base
3. Convert the number of moles of base to the number of moles of acid, using your mole ratio
4. Divide the number of moles by the volume of acid used in titration

TA-DAAA!! That value is your concentration, or molarity.

*Note: Be sure to use dimensional analysis if unit conversion is necessary

Open Ended

If a 25mL solution of HCl is neutralized by 18mL of a 1.0M NaOH solution, what is the concentration of the HCl solution?

Answer:

You should have gotten 0.72 mol/L

A Glimpse into Chapter 5

Let's use what we already know about chemical reactions and balanced chemical equations to solve a problem with Hess's Law.

 $\Delta H_{rxn}=\Delta H_{f\left(products\right)}-\Delta H_{f\left(reagents\right)}$  

Open Ended

Using Hess's Law, find the enthalpy of this reaction:

2NO(g) + O₂(g) --> 2NO₂(g)

You are given these standard enthalpy of formation values:

O₂(g): 0 kJ/mol

NO(g): 90.25 kJ/mol

NO₂(g): 33.18 kJ/mol

Answer:

-114.1 kJ