Chapter 3
Calculations with Chemical Formulas and Equations

1.Mass and moles of substance

• Molecular wt/formula wt/molar mass
• The mole concept.

2. Determining chemical formulas

• Mass percentages
• Elemental Analysis
• Determining formulas

3. Stoichiometry

• Molar interpretation of equations
• Amounts of substance in a chemical reaction
• Limiting reactant and theoretical and % yield

Objectives. Be able to:

• balance chemical equations
• recognize and predict the products of: combustion, combination and decomposition reactions.
• calculate the atomic weight of an element from the relative abundances and masses of its isotopes.
• relate number of moles, mass in grams, and number of atoms, ions, or molecules.
• calculate empirical and molecular formulas from appropriate data.
• calculate the mass of product or reactant used in a chemical reaction.
• determine the limiting reagent and calculate the percent yield in a reaction.

1. Mass and moles of substance

Molecular wt/formula wt/molar mass

The Atomic Mass Scale

the Atomic Mass on the Periodic Table is the average atomic mass of all isotopes of that element as compared to the defined mass for carbon-12 of exactly 12 amu.

Formula and Molecular Weights (Molar Mass)

formula weight is the sum of the atomic weights of each atom in a chemical formula. Frequently used for ionic compounds (metal + anion)

eg. MgCl₂

molecular weight is the sum of the atomic weights of each atom in a molecular formula. (nonmetals combining)

ex. N₂O₂

The mole concept.

The number of atoms contained in exactly 12 grams of Carbon-12 atoms.

The number of particles (atoms or molecules) contained in a sample of element or compound, that has a mass equal to the atomic or molecular weight.

6.02*10²³ of anything!

602,000,000,000,000,000,000,000. of anything!

Examples:

1. Suppose we have 5.75 moles of magnesium (atomic wt. = 24.3 g/mol). What is its mass?

1 mol Fe atoms = 6.02*10²³ Fe atoms = 55.85 g Fe

Use these equivalencies to determine:

1. the mass in grams of 6.885 mol of Fe

2. . the number of moles of Fe atoms in 255 grams of Fe

3. the number of atoms of Fe in 255 grams of Fe

2. Determining chemical formulas

• Mass percentages
• Determining formulas

Percentage Composition from Formulas-

once the molecular or formula weight is known then the mass (weight) percent of each element may be determined.

Examples

1. Urea, CH₄N₂O, and ammonium sulfate (NH₄)₂SO₄ are both used as agricultural fertilizers. Which one contains the higher weight percent of nitrogen?

2. How many grams of carbon in 83.5 g CH₂O?

3. Calculate the percent composition of butane, C₄H₁₀.

• Elemental Analysis

Combustion Analysis

Measurement of combustion products allows determination of mass percents and therefore empirical formulas.

Example: Vanillin, the flavor in vanilla, contains only C, H, and O. When 1.05 g of this substance is completely combusted, 2.43 g of CO₂ and 0.500 g of H₂O is produced. Determine the % C, H, and O in the compound vanillin.

Determining formulas

• Molecular Formula from Empirical Formula

By comparing the ratio of the weights of the molecular formula to the empirical formula, the ratio of the formulas may be determined.

Example:

The empirical formula for acetylene is CH, the molecular weight of acetylene is 26 g/mol. Determine the molecular formula.

empirical weight= ?

Therefore the molecular formula. is 2 times the empirical formula. Write the molecular formula for acetylene.

More Examples:

Process:

• some way, find the mass of each element
• then find the moles of each using the atomic mass for the element
• last, find the mole ratio to give you the Empirical Formula.
• if the molecular formula is needed, use the empirical weight and the molecular weight(often given) to find the ratio then multiply the subscripts on the EF by that number. Occasionally, you may need to multiply by two or three if the ratios round to halves, or thirds.

1. Determine the empirical formula of vanillin from the % composition calculated in the combustion example.
   
   
   
   
2. Benzoic acid is a white, crystalline powder used as a food preservative. The compound contains 68.8% C, 5.0% H, and 26.2% O by mass. What is its empirical formula?
   
   
   
   
   
   
   
   
3. Suppose the empirical formula of a compound is CH₂O and its "true" molecular weight is 60.0 g/mol. The molar weight of the empirical formula (the "empirical weight") is only 30.0 g/mol. This would imply that the "true" molecular formula is actually the empirical formula doubled, or ____?

3. Stoichiometry

Molar interpretation of equations

Chemical Reactions- what do they represent?

Moles A ——> moles B calculations require the mole ratio from a balanced equation. I call this the 'bridge".

In the Haber process, hydrogen gas reacts with nitrogen gas to form ammonia. Write the balaced equation and calculate how many moles of H₂ is required to react with 4.67 moles of N₂ ?

Amounts of substance in a chemical reaction

Mass A —> moles A —> moles B —> mass B

1. How many grams of HCl are required to react with 5.00 grams manganese dioxide according to this equation?

2. How many grams of water are produced when 1.00 x 10² g of gasoline (C₈H₁₈) are burned in an automobile engine?

Limiting reactant and theoretical and % yield

Limiting reactants are often calculated by using each known amount and calculating how much of the product is formed. The reactant that gives the least amount of product is the limiting reactant and tells you the amount produced. Typically, you will have two knowns and one unknown.

Theoretical Yields-the maximum quantity of product based on the stoichiometry of the balanced equation for the reaction.

Actual Yield- the actual experimentally determined quantity of product produced in a reaction.

Examples:

1. Zinc metal reacts with hydrochloric acid by the following reaction.

Zn(s) + 2HCl ——> H₂(g) + ZnCl₂(aq)

If 0.30 mol Zn is added to hydrochloric acid containing 0.52 mol HCl, how many moles of H₂ are produced?

2. To illustrate the calculation of percentage yield, recall that the theoretical yield of H₂ in the previous example was 0.26 H₂. If the actual yield of the reaction had been 0.22 g H₂, then the % yield is___?

Added Topic from Ch. 6.

Energy and its Units

Energy can be in many forms:

• Radiant Energy -Electromagnetic radiation.
• Thermal Energy - Associated with random motion of a molecule or atom.
• Chemical Energy - Energy stored within the structural limits of a molecule or atom.

energy units-

• joule- a mass of 2 kg, moving at a velocity of 1 m/s possesses a kinetic energy of 1 J.
• 1 J= 1 kg*m²/s² (= N*m)

calorie- traditional unit of energy (1g water 1°C). Now it is defined in terms of the Joule.

1 cal=4.184 J

• Kinetic Energy is the energy associated with an object by virtue of its motion. E_K = ¹/₂ mv²
• Potential Energy is the energy an object has by virtue of its position in a field of force. E_P=mgh
• Internal Energy is the sum of the kinetic and potential energies of the particles making up a substance.

Total Energy = E_K + E_P + U

Examples

In chemical reactions, heat is often transferred from the "system" to its "surroundings," or vice versa.

• thermochemistry-the study of energy changes with chemical reactions.
• work- energy used moving objects against a force, w= F * d
• heat- energy transfer from one object to another.
• system- that which is under study, e.g.. a reaction.
• surroundings- everything outside of the system
• universe- system + surroundings.

Heats of Reaction

• Heat is denoted by the symbol q.
• The sign of q is positive if heat is absorbed by the system.
• The sign of q is negative if heat is evolved by the system.
• An exothermic process is a chemical reaction or physical change in which heat is evolved (q is negative).
• An endothermic process is a chemical reaction or physical change in which heat is absorbed (q is positive).

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Updated Jan. 3, 2004. Questions or comments on this Web site should go to Robin Terjeson.