Topic 16 Topic 16 Topic 16: Stoichiometry Basic Concepts Additional Concepts Table of Contents Topic...

Topic 16Topic 16

Topic 16: Stoichiometry

Basic Concepts

Additional Concepts

Table of ContentsTable of ContentsTopic 16Topic 16

• Using the methods of stoichiometry, we can measure the amounts of substances involved in chemical reactions and relate them to one another.

Stoichiometry

Stoichiometry: Basic ConceptsStoichiometry: Basic ConceptsStoichiometry: Basic ConceptsStoichiometry: Basic Concepts

• For example, a sample’s mass or volume can be converted to a count of the number of its particles, such as atoms, ions, or molecules.

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• Atoms are so tiny that an ordinary-sized sample of a substance contains so many of these submicroscopic particles that counting them by grouping them in thousands would be unmanageable.

Stoichiometry


• Even grouping them by millions would not help.

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• The group or unit of measure used to count numbers of atoms, molecules, or formula units of substances is the mole (abbreviated mol).

Stoichiometry


• The number of things in one mole is 6.02 x 1023. This big number has a short name: the Avogadro constant.

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• The most precise value of the Avogadro constant is 6.0221367 x 1023. For most purposes, rounding to 6.02 x 1023 is sufficient.

• Methanol is formed from CO2 gas and hydrogen gas according to the balanced chemical equation below.

Molar Mass

Stoichiometry: Basic ConceptsStoichiometry: Basic ConceptsStoichiometry: Basic ConceptsStoichiometry: Basic ConceptsTopic 16Topic 16

Molar Mass


• Suppose you wanted to produce 500 g of methanol.

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• How many grams of CO2 gas and H2 gas would you need? How many grams of water would be produced as a by-product?

• Those are questions about the masses of reactants and products.

• But the balanced chemical equation shows that three molecules of hydrogen gas react with one molecule of carbon dioxide gas.

Molar Mass


• The equation relates molecules, not masses, of reactants and products.

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• Like Avogadro, you need to relate the macroscopic measurements—the masses of carbon dioxide and hydrogen—to the number of molecules of methanol.

Molar Mass


• To find the mass of carbon dioxide and the mass of hydrogen needed to produce 500 g of methanol, you first need to know how many molecules of methanol are in 500 g of methanol.

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• Average atomic masses of the elements are given on the periodic table.

Molar Mass of an Element


• For example, the average mass of one iron atom is 55.8 u, where u means “atomic mass units.”

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• The atomic mass unit is defined so that the atomic mass of an atom of the most common carbon isotope is exactly 12 u, and the mass of 1 mol of the most common isotope of carbon atoms is exactly 12 g.





• The mass of 1 mol of a pure substance is called its molar mass.

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• The molar mass is the mass in grams of the average atomic mass.



• If an element exists as a molecule, remember that the particles in 1 mol of that element are themselves composed of atoms.

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• For example, the element oxygen exists as molecules composed of two oxygen atoms, so a mole of oxygen molecules contains 2 mol of oxygen atoms.



• Therefore, the molar mass of oxygen molecules is twice the molar mass of oxygen atoms: 2 x 16.00 g = 32.00 g.

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• The mass of an iron bar is 16.8 g. How many Fe atoms are in the sample?

Number of Atoms in a Sample of an Element


• Use the periodic table to find the molar mass of iron.

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• Use the periodic table to find the molar mass of iron. The average mass of an iron atom is 55.8 u.

• Then the mass of 1 mol of iron atoms is 55.8 g.

• To convert the mass of the iron bar to the number of moles of iron, use the mass of 1 mol of iron atoms as a conversion factor.


• Now, use the number of atoms in a mole to find the number of iron atoms in the bar.

Number of Atoms in a Sample of an Element

• Simplify the expression above.

Stoichiometry: Basic ConceptsStoichiometry: Basic ConceptsStoichiometry: Basic ConceptsStoichiometry: Basic ConceptsTopic 16Topic 16 Number of Atoms in a Sample of an

Element

• Covalent compounds are composed of molecules, and ionic compounds are composed of formula units.

Molar Mass of a Compound


• The molecular mass of a covalent compound is the mass in atomic mass units of one molecule.

• Its molar mass is the mass in grams of 1 mol of its molecules.

• The formula mass of an ionic compound is the mass in atomic mass units of one formula unit.



• Its molar mass is the mass in grams of 1 mol of its formula units.

• How to calculate the molar mass for ethanol, a covalent compound, and for calcium chloride, an ionic compound, is shown.

• Ethanol, C2H6O, a covalent compound.



• Calcium chloride, CaCl2, an ionic compound.



• The mass of a quantity of iron(III) oxide is 16.8 g. How many formula units are in the sample?

Number of Formula Units in a Sample of a Compound


• Use the periodic table to calculate the mass of one formula unit of Fe2O3.


• Therefore, the molar mass of Fe2O3 (rounded off) is 160 g.

Number of Formula Units in a Sample of a Compound

• Now, multiply the number of moles of iron oxide by the number in a mole.

Stoichiometry: Basic ConceptsStoichiometry: Basic ConceptsStoichiometry: Basic ConceptsStoichiometry: Basic ConceptsTopic 16Topic 16 Number of Formula Units in a Sample

of a Compound

• What mass of water must be weighed to obtain 7.50 mol of H2O?

Mass of a Number of Moles of a Compound


• The molar mass of water is obtained from its molecular mass.

• The molar mass of water is 18.0 g/mol.

• Use the molar mass to convert the number of moles to a mass measurement.

Stoichiometry: Basic ConceptsStoichiometry: Basic ConceptsStoichiometry: Basic ConceptsStoichiometry: Basic ConceptsTopic 16Topic 16 Mass of a Number of Moles of a

Compound

• The concept of molar mass makes it easy to determine the number of particles in a sample of a substance by simply measuring the mass of the sample.


• The concept is also useful in relating masses of reactants and products in chemical reactions.

Mass of a Number of Moles of a Compound

• Ammonia gas is synthesized from nitrogen gas and hydrogen gas according to the balanced chemical equation below.

Predicting Mass of a Reactant




• How many grams of hydrogen gas are required for 3.75 g of nitrogen gas to react completely?

• Find the number of moles of N2 molecules by using the molar mass of nitrogen.

• To find the mass of hydrogen needed, first find the number of moles of H2 molecules needed to react with all the moles of N2 molecules.



• The balanced chemical equation shows that 3 mol of H2 molecules react with 1 mol of N2 molecules.

• Multiply the number of moles of N2 molecules by this ratio.



• The units in the expression above simplify to moles of H2 molecules.

• To find the mass of hydrogen, multiply the number of moles of hydrogen molecules by the mass of 1 mol of H2 molecules, which is 2.00 g.



• What mass of ammonia is formed when 3.75 g of nitrogen gas react with hydrogen gas according to the balanced chemical equation below?

Predicting Mass of a Product


• The amount of ammonia formed depends upon the number of nitrogen molecules present and the mole ratio of nitrogen and ammonia in the balanced chemical equation.

• The number of moles of nitrogen molecules is given by the expression below.





• To find the mass of ammonia produced, first find the number of moles of ammonia molecules that form from 3.75 g of nitrogen.

• Use the mole ratio of ammonia molecules to nitrogen molecules to find the number of moles of ammonia formed.



• Use the molar mass of ammonia, 17.0 g, to find the mass of ammonia formed.

Using Molar Volumes in Stoichiometric Problems


• In terms of moles, Avogadro’s principle states that equal volumes of gases at the same temperature and pressure contain equal numbers of moles of gases.

• The molar volume of a gas is the volume that a mole of a gas occupies at a pressure of one atmosphere (equal to 101 kPa) and a temperature of 0.00°C.

Using Molar Volumes in Stoichiometric Problems


• Under these conditions of STP, the volume of 1 mol of any gas is 22.4 L.

• Like the molar mass, the molar volume is used in stoichiometric calculations.

Using Molar Volume


• In the space shuttle, exhaled carbon dioxide gas is removed from the air by passing it through canisters of lithium hydroxide. The following reaction takes place.

• How many grams of lithium hydroxide are required to remove 500.0 L of carbon dioxide gas at 101 kPa pressure and 25.0°C?

Using Molar Volume


• The volume of gas at 25°C must be converted to a volume at STP.

• Now, find the number of moles of CO2 gas as below.

Using Molar Volume


• The chemical equation shows that the ratio of moles of LiOH to CO2 is 2 to 1.

• Therefore, the number of moles of lithium hydroxide is given by the expression below.

• To convert the number of moles of LiOH to mass, use its molar mass, 23.9 g/mol.

Using Molar Volume


Ideal Gas Law


• Exactly how the pressure P, volume V, temperature T, and number of particles n of gas are related is given by the ideal gas law shown here.

PV = nRT

Ideal Gas Law


• The value of the constant R can be determined using the definition of molar volume.

• At STP, 1 mol of gas occupies 22.4 L. Therefore, when P = 101.3 kPa, V = 22.4 L, n = 1 mol, and T = 273.15 K, the equation for the ideal gas law can be shown as follows.

Ideal Gas Law


• Now, we can solve for R.

Using the Ideal Gas Law


• How many moles are contained in a 2.44-L sample of gas at 25.0°C and 202 kPa?

• Solve the ideal gas law for n, the number of moles.



• First, find the volume that 2.44 L of a gas would occupy at STP.



• Then, find the number of moles in this volume.

• 0.200 mol is close to the calculated value.

Determining Mass Percents


• The formula for geraniol (the main compound that gives a rose its scent) is C10H18O.



• The formula shows that geraniol is comprised of carbon, hydrogen, and oxygen.

• Because all these elements are nonmetals, geraniol is probably covalent and comprised of molecules.



• In addition, the formula C10H18O tells you that each molecule of geraniol contains ten carbon atoms, 18 hydrogen atoms, and one oxygen atom.

• In terms of numbers of atoms, hydrogen is the major element in geraniol.



• How can you tell whether it is the major element by mass?

• You can answer this question by determining the mass percents of each element in geraniol.

Stoichiometry: Basic ConceptsStoichiometry: Basic ConceptsStoichiometry: Basic ConceptsStoichiometry: Basic ConceptsTopic 16Topic 16 Mass Percents of Elements in Geraniol

• This pie graph shows the composition of geraniol in terms of mass percents of the elements.

Mass Percents of Elements in Geraniol


• Suppose you have a mole of geraniol. Its molar mass is 154 g/mol.

• Of this mass, how many grams do the carbon atoms contribute?

• The formula shows that one molecule of geraniol includes ten atoms of carbon.

• Therefore, 1 mol of geraniol contains 10 mol of carbon.



• Multiply the mass of 1 mol of carbon by 10 to get the mass of carbon in 1 mol of geraniol.

• Now, use this mass of carbon to find the mass percent of carbon in geraniol.



• The mass percents of the other elements are calculated below in a similar fashion.

• Mass of hydrogen in 1 mol geraniol:



• Mass of oxygen in 1 mol geraniol:

Determining Chemical Formulas


• The formula of a compound having the smallest whole-number ratio of atoms in the compound is called the empirical formula.

• The empirical formula of this unknown compound is NaClO4.

Basic Assessment QuestionsBasic Assessment Questions

Question 1

Determine the number of atoms in 45.6 g gold, Au.

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Answer

1.39 x 1023 Au atoms

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Question 2

Determine the number of atoms in 17.5 g copper(II) oxide, CuO.

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Answer

0.220 mol CuO

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Question 3

Determine the mass of 1.25 mol aspirin C9H8O4.

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Answer

225g C9H8O4

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Question 4

What mass of sulfur must burn to produce 3.42 L of SO2 at 273°C and 101 kPa? The

reaction is

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Answer

2.45 g S

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Stoichiometry: Additional ConceptsStoichiometry: Additional Concepts Stoichiometry: Additional ConceptsStoichiometry: Additional Concepts Topic 16Topic 16

Additional Concepts

Stoichiometry: Additional ConceptsStoichiometry: Additional Concepts Stoichiometry: Additional ConceptsStoichiometry: Additional Concepts

Stoichiometric Calculations• There are three basic stoichiometric

calculations: mole-to-mole conversions, mole-to-mass conversions, and mass-to-mass conversions.

• All stoichiometric calculations begin with a balanced equation and mole ratios.

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Stoichiometric mole-to-mole conversion • How can you determine the number of moles

of table salt (NaCl) produced from 0.02 moles of chlorine (Cl2)?


Stoichiometric mole-to-mole conversion

• First, write the balanced equation.

• Then, use the mole ratio to convert the known number of moles of chlorine to the number of moles of table salt. Use the formula below.

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Stoichiometric Mole-to-Mass Conversion

• A mole-to-mass conversion allows you to calculate the mass of a product or reactant in a chemical reaction given the number of moles of a reactant or product.

• The following reaction occurs in plants undergoing photosynthesis.

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• How many grams of glucose (C6H12O6) are produced when 24.0 moles of carbon dioxide reacts in excess water?

• Determine the number of moles of glucose produced by the given amount of carbon dioxide.

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• Multiply by the molar mass.

• 721 grams of glucose is produced from 24.0 moles of carbon dioxide.

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Stoichiometric Mass-to-Mass Conversion

• In this calculation, you can find the mass of an unknown substance in a chemical equation if you have the balanced chemical equation and know the mass of one substance in the equation.

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• How many grams of sodium hydroxide (NaOH) are needed to completely react with 50.0 grams of sulfuric acid (H2SO4) to form sodium sulfate (Na2SO4) and water?

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• Write the balanced equation.



• Convert grams of sulfuric acid to moles NaOH.

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• Calculate the mass of NaOH needed.

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• 50.0 grams of H2SO4 reacts completely with 40.8 grams of NaOH.


Limiting Reactants

• Rarely are the reactants in a chemical reaction present in the exact mole ratios specified in the balanced equation.

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• Usually, one or more of the reactants are present in excess, and the reaction proceeds until all of one reactant is used up.

• The reactant that is used up is called the limiting reactant.


Limiting Reactants• The limiting reactant limits the reaction and,

thus, determines how much of the product forms.

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• The left-over reactants are called excess reactants.

• How can you determine which reactant in a chemical reaction is limited?

• First, find the number of moles of each reactant by multiplying the given mass of each reactant by the inverse of the molar mass.


Determining the Limiting Reactant

• In the reaction below, 40.0 g of sodium hydroxide (NaOH) reacts with 60.0 g of sulfuric acid (H2SO4).

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• To determine the limiting reactant, calculate the actual ratio of available moles of reactants.

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• You can see that when 0.5 mol H2SO4 has reacted, all of the 1.00 mol of NaOH would be used up.

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• Some H2SO4 would remain unreacted. Thus, NaOH is the limiting reactant.

• So, is available. Compare this

ratio with the mole ratio from the balanced

equation: , or



• To calculate the mass of Na2SO4 that can form from the given reactants, multiply the number of moles of the limiting reactant (NaOH) by the mole ratio of the product to the limiting reactant and then multiply by the molar mass of the product.

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Determining the Limiting ReactantTopic 16Topic 16

• 71.0 g of Na2SO4 can form from the given amounts of the reactants.

Additional Assessment QuestionsAdditional Assessment Questions

Question 1 Topic 16Topic 16

Balance the following equation. How many moles of KClO3 are needed to produce 50

moles of O2?


AnswerTopic 16Topic 16


Question 2Topic 16Topic 16

Calculate the mass of sodium chloride (NaCl) produced when 5.50 moles of sodium reacts in excess chlorine gas.



321g NaCl



Determine the mass of copper needed to react completely with a solution containing 12.0 g of silver nitrate (AgNO3).



2.24g Cu



Aluminum reacts with chlorine to produce aluminum chloride.

Balance the equation.

Answer 4a

Question 4a

Additional Assessment QuestionsAdditional Assessment QuestionsTopic 16Topic 16

If you begin with 3.2 g of aluminum and 5.4 g of chlorine, which is the limiting reactant?

Answer 4b

Question 4b

Additional Assessment QuestionsAdditional Assessment QuestionsTopic 16Topic 16

Cl2

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