Learning objectives
- Explain the mole concept, and convert between grams, moles, and atoms and molecules.
- Determine mass percent composition of a sample from experimental data.
- Determine mass percent composition of a compound from its formula.
- Determine empirical formula of a compound from its mass percent composition.
- Use chemical equations to predict amounts of reactant consumed or product produced in a chemical change.
- Define limiting reagent and identify the limiting reagent in a chemical equation.
- Define and distinguish theoretical yield, actual yield, and percent yield. Compute percent yield from actual and theoretical yields.
- Define molarity. Relate molarity, moles of solute, and liters of solution.
- Explain how a solution of a desired concentration can be prepared from solid solute or from a more concentrated stock solution.
Lecture outline
Counting molecules by weighing
moles -is, f. a shapeless mass. TRANSF., 1. a mass of men, a large number; 2. greatness, might, power; 3. trouble, difficulty -Cassell's Latin Dictionary | |
- Why use moles?
- many properties depend on the number of molecules in the sample, not on the mass of the sample. How can the number of molecules in the sample be measured?
- solution: convert sample mass to daltons to molecules, using the molecular weight
- now you can count molecules in a pure sample just by weighing the sample.
- problem: daltons are very small units, and inconvenient; can we convert grams to molecules without using them?
- solution: define a new unit, the mole (SI unit for amount of substance)
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The official definition is "1 mole of particles is equal to the number of atoms in exactly 12g of carbon-12". | |
- Defining moles
- 1 mole of molecules has a mass equal to the molecular weight in grams.
- examples
- 1 mole H2O is the number of molecules in 18.015 g H2O
- 1 mole H2 is the number of molecules in 2.016 g H2.
- 1 mole of atoms has a mass equal to the atomic weight in grams.
- 1 mole of particles = 6.02214 x 1023 particles
for any substance!
- Prove this by converting 1 mole to grams to daltons to particles for any substance.
- vocabulary
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molar mass is the mass of one mole of a substance
- bridge between moles and grams in unit conversion problems
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Avogadro's number is the number of molecules in one mole for any substance
- bridge between molecules and moles in unit conversion problems
Using chemical formulas
- molecular formulas give atom-to-atom and mole-to-mole ratios
- example: molecular formula C6H12O6
atom-to-atom ratios |
atom-to-molecule ratios |
mole-to-mole ratios (elements) |
mole-to-mole ratio (compound) |
6 atoms C 12 atoms H
6 atoms C 6 atoms O
12 atoms H 6 atoms O
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6 atoms C 1 molecule
12 atoms H 1 molecule
6 atoms O 1 molecule
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6 mol C 12 mol H
6 mol C 6 mol O
12 mol H 6 mol O
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6 mol C 1 mol C6H12O6
12 mol H 1 mol C6H12O6
6 mol O 1 mol C6H12O6
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- problems that ask you to relate one substance to another require mole-to-mole ratios
- examples
- How many grams of H2 can be obtained from the electrolysis of 10.0 g of H2O?
- How many grams of CuO can be made from a piece of copper wire weighing 0.2134 g?
- 2.04 g of carbon reacts with 5.44 g of O2 to form 7.48 g of compound. How many atoms of O per atom of C are in this compound?
Chemical formulas and elemental composition
- mass percent: percent of total sample mass contributed by a particular component
- determine experimentally by decomposing sample into components and weighing the separate components
- determining water of hydration
- combustion analysis of hydrocarbons
- finding element mass percents from a chemical formula
- strategy: convert the mole fraction of element in compound to a mass fraction
- procedure
- Write a subscript X from the formula as (X mol element / 1 mol compound)
- Convert moles of element to grams (using the atomic weight)
- Convert moles of compound to grams (using the molar mass)
- Multiply by 100%
- examples
- To how many significant figures must you determine the percentage of carbon in a drug sample to distinguish cocaine (C17H21O4N) from aspirin (C9H8O4)?
- Vitamin B12 is 4.34% Co. If there is only one atom of Co per molecule of vitamin, what is the molar mass of vitamin B12?
- finding empirical formulas from element mass percents
- Write the mass percent as a mass (mass percent is just mass per 100 g sample).
- Convert each mass to moles.
- Divide each molar amount by the smallest molar amount.
- Round the mole ratios to the nearest whole number or simple fraction. Use significant figures to guide your choice of whole number or fraction!
- If necessary, scale the ratios so that all are whole numbers. These are the subscripts in the empirical formula.
- examples
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elemental analysis of a pure compound isolated from tea leaves gave the following results: 49.48% C, 5.19% H, 28.85% N, 16.48% O. What is the empirical formula of the compound?
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|
g element per 100 g sample |
moles element per 100 g sample |
mole ratio |
simplified ratio |
49.48 g C |
4.11952 mol C |
3.99939 |
4 |
5.19 g H |
5.1490 mol H |
4.9988 |
5 |
28.85 g N |
2.05973 mol N |
1.99966 |
2 |
16.48 g O |
1.03004 mol O |
1 |
1 |
...The empirical formula is C4H5N2O (it's caffeine).
- What is the empirical formula of a purified drug sample that is 74.27% C, 7.79% H, 12.99% N, and 4.95% O?
- What is the empirical formula of an iron oxide that 70.0% Fe and 30.0% O?
- What is the molecular formula of a compound that is 5.93% H and 94.07% O, with molar mass 34.015 g?
Using Chemical Equations
- predicting amount of substance produced or consumed in a chemical reaction
- coefficients in balanced equation relate moles of one substance to moles of another substance in the reaction
- general problem format: Substances A and B are involved in a chemical reaction. An amount of A is given. Find the amount of B that is produced or consumed when A completely reacts.
- strategy:
- Write a balanced chemical equation for the reaction.
- Find moles of A from given information.
- Convert moles of A to moles of B using mole ratios from the balanced chemical equation.
- Convert moles of B to desired units.
- examples
- Oxygen gas can be produced in the laboratory by decomposition of hydrogen peroxide (H2O2):
2 H2O2(aq)
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2 H2O(l) + O2(g)
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How many kg of O2(g) can be produced from 1.0 kg of hydrogen peroxide?
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How many grams of oxygen gas are required to completely burn exactly 1 kg of glucose (C6H12O6)?
- How many pounds of CO2 are produced by burning 1 gallon (5.6 lbs) of octane (C8H18)?
- Estimate sulfur dioxide emissions (in tons per year) for a power plant that annually burns 2.5 million tons of coal that is 3% sulfur by mass.
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Limiting reagent demo from Carnegie-Mellon University | |
- predicting the amount of product produced (theyield) from amounts of more than one reactant
- if reactants aren't mixed in the right mole ratio, yield is limited by one of the reactants
- strategy
- compute yield for each reactant
the lowest yield is the
theoretical yield
the reactant giving the lowest yield is the
limiting reactant.
- examples
-
Ethanol (C2H5OH) is synthesized for industrial use by the following reaction, carried out at very high pressure:
C2H4(g) + H2O(g)
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C2H5OH
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What is the maximum amount of ethanol that can be produced when 1.0 kg of ethylene (C2H4) and 1.0 kg of steam are placed in the reaction vessel?
- Some of the acid in acid rain is produced by the following reaction:
3 NO2(g)+ H2O(l)
2HNO3(aq) + NO(g)
A falling raindrop weighing 0.05 g comes into contact with
1 mg of NO2. How much HNO3 can be produced?
- why doesn't actual yield = theoretical yield?
- impurities in reactants
- mechanical losses
- side reactions
synthesis of 2, 4, 5-T
- reversible reactions
H2(g) + Cl2(g)
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2 HCl(g)
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| actual yield close to theoretical yield
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H2(g) + I2(g) l 2 HI(g)
| actual yield is much less than theoretical yield! |
- calculating percentage yield
- the actual yield must be given
- compute the theoretical yield
- percentage yield = (actual yield/theoretical yield) x 100%
- examples
- 0.12 g of ozone is produced per gram of oxygen gas exposed to an electric arc. What is the percent yield of ozone?
- The fertilizer ammonium nitrate is synthesized from ammonia and nitric acid. If 17 tons of ammonia produced 63 tons of fertilizer, what is the percent yield?
- predicting the amount of excess reactants
- strategy
- find how many moles of each reactant is present before the reaction
- identify the limiting reactant
- find how much of each reactant is consumed by converting moles of limiting reactant to moles of each of the nonlimiting reactants
- final moles of reactant = initial moles - moles consumed
- example
- The following reaction is used to extract gold from pretreated gold ore:
2 Au(CN)2-(aq) + Zn(s)
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2 Au(s) + Zn(CN)42-(aq)
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If 0.654 g of powdered Zn is added to a solution that contains 2.52 g of Au(CN)2-, what masses of reactants will be left over after the reaction is complete?
- caveats about interpreting these calculations
- chemical equations give only mole ratios between reactants and products
- equations are macroscopic - they don't represent actual molecular level events!
- example: reactions with intermediates
- equations can depict impractical or impossible reactions
- example: formation reactions for organic molecules
- some reactions don't run to completion: watch for the double harpoon
General Chemistry Online! The moleCopyright © 1997-2005 by Fred Senese Comments & questions to fsenese@frostburg.edu Last Revised 02/23/18.URL: http://antoine.frostburg.edu/chem/senese/101/moles/print-index.shtml
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