chemical math. 1.1.1 apply the mole concept to substances. apply: use an idea, equation principle,...

THE MOLEChemical Math

1.1.1 Apply the mole concept to substances.

Apply: Use an idea, equation principle, theory or law in a new situation.

IB Core

What is it? How many eggs are in a

dozen?


Size matters

Atoms are VERY small, how small? Take a ping pong ball an

placed it in the center of a soccer stadium. This is the atoms nucleus.

Then take a pin and stand on the very edge of the stadium. The pin head is the electron.

Dealing with VERY small things To count small things we need a large number

1 dozen atoms is only 12 atoms

We need a new number. Avogadro's Number

The mole: 6.02 x 10 23 1 mole atoms = 6.02 x 10 23 atoms 3 moles of atoms = 3 (6.02 x 10 23 ) atoms



Understanding the number• If you ordered a mole of donuts instead of a

dozen, that would be enough to give every person in the world over 9 trillion donuts.

• The Earth is estimated to be about 4.54 billion years old. That is approximately 1.43 x 1017 seconds, still much less than a mole.

• Spreading a mole of marbles over the Earth would produce a layer almost five kilometers thick

• If you traveled a mole in inches, you would be able to cross the galaxy and back eight times, or go around the Earth 300 trillion times.


The Sahara Desert is about 1500 km north to south and 4000 km east to west.

If the average depth of sand throughout is 10 m, and there were about 1000 grains of sand in each cm3, then the Sahara Desert would contain about 6 x 1022 grains of sand.

This is still one tenth of a mole. This means there are more atoms of

carbon in a 12 g sample (one mole) then there are grains of sand in the Sahara Desert

IB Core

1.1.2 Determine the number of particles and the amount of substance (in moles).

Determine: Find the only possible answer. (Obj. 3)

Using Avogadro's Number How many Hydrogen and Oxygen atoms are

there in 1 mol of water? What is the total # of atoms?

H2O Ratio 1:2: There are 2 Hydrogen atoms for

every water molecule. 1 mol of water molecules has 2 moles of hydrogen

atoms 2 mol Hydrogen x (6.02 x 10 23 )atoms/mol = 12.04 x 10 23 hydrogen atoms.

Ratio 1:1 There is 1 Oxygen atom for ever water molecule. 1 mol oxygen 6.02 x 10 23 atoms/mol = 6.02 x 10 23 oxygen atoms / mol


Using 1 mol of substance, how many atoms? HCl

O3

CH4

There are 2 mols of atoms: 1.20*1024 atoms



Click for answers


IB Core1.2.1 Define the terms relative

atomic mass (Ar) and relative molecular mass (Mr).

Define: Give the precise meaning of a word, phrase or physical quantity. (Obj 1)

Relative Atomic Mass & Relative Molecular Mass

Relative Atomic Mass (Ar): Weighted mean mass of all naturally occurring isotopes

of an element. The number is the ratio of the average mass per atom to 1/12 of an atom of the C-12 isotope.

Relative Molecular Mass (Mr) The mass of a molecule. Indicates how heavy the

molecule is compared to the C-12 isotope.

Relative things have NO UNITS!

But!! Atomic Mass does! (g/mol) or (g mol-1)

You find these values on the Periodic Table

To get this value, just use the Ar from

above and add g/mol to the end

IB Core1.2.2 Calculate the mass of one

mole of a species from its formula.

Calculate: Find a numerical answer showing the relevant stages in the working (unless instructed not to do so).

Molar Mass

Molar mass (M) is the mass of one mol of atoms (g/mol)

For compounds or Elements with multiple atoms: Add the atomic mass

of all the atoms in the compound.

What is the Molar mass of H2O?

H: 1.008 g/mol O: 16.00 g/mol

M = 2(1.008)g/mol + 1(16.00) g/mol =18.02 g/mol

Number of Atoms

involved

Atomic Mass(On P-table)

Units...Don’t be lazy!

Final Molar Mass of Water

Sig. Figs

Questions

What is the Molar Mass of:

CO2

CH4

Sodium Sulphate

Questions What is the Molar Mass of: Potassium Chloride

Iron(III) Oxide

Copper(II) Nitrate

IB Core

1.2.3 Solve problems involving the relationship between the amount of substance in moles, mass and molar mass.

Solve: Obtain an answer using algebraic and/or numerical methods.

1.2.3 Solve problems involving the relationship between the amount of

substance in moles, mass and molar mass.Stoichiometry Time!

Time to learn what stoichiometry is all about!

Yee-haw!!Definition of stoichiometry: The

relationships among the quantities of reactants and products involved in chemical reactions.

1.2.3 Solve problems involving the relationship between the amount of

substance in moles, mass and molar mass.

unit desired unitgiven

unit desiredunit x Given

• When you have something to start with, and you know what unit youare after, you can solve the problem!!• Be sure to cancel out units as you go through.

Special Note

1 mol of ANY IDEAL GAS occupies a

volume of 22.4 dm3 at S.T.P.

You may also see it done this way...

Formula n= m

M n = # of moles (mol)

m = mass (g)

MM = Molar Mass (g/mol)

Oxygen8O

15.999

1.2.3 Solve problems involving the relationship between the amount of substance in moles, mass, and molar mass.

Sample problems:

If you have 4.904 g of sulfuric acid, how many moles would you have?

You have 2.00 mols of carbon dioxide. How many grams of carbon dioxide do you have?

Answers to previous slide

Sulfuric acid is H2SO4 . So the molar mass would be (2 x 1.01) + (32.07) + (4 x 16.00) = 98.09 g mol-1 4.904 g H2SO4 x = 0.04999 mols

Carbon dioxide is CO2. So 12.01 + (2 x 16.00) = 44.01 g mol-1.

2.0 mol CO2 x = 88 g CO2

H2SO4 g 98.09

H2SO4 mol 1

CO2 mol 1

CO2 g01.44

1.2.3 Solve problems involving the relationship between the amount of substance in moles, mass, and molar

mass.

The combustion of Hydrogen gas and Oxygen. 1) Determine the product and write the

chemical equation for the reaction 2) Balance the equation 3) What is the ratio of Oxygen to Hydrogen?

If I react 24 g of Hydrogen gas with oxygen, 1) How many grams of oxygen will I need? 2) How many grams of product will I make?

Answer 2H2 + O2 → 2H2O

Ratio:

You will need 380 grams of oxygen.

You will make 214 grams (210 using sig figs) of product (H2O)

H2 mol 2

O2 mol 1

IB Core Objective

1.2.4 Distinguish between the terms empirical formula and molecular formula.

Distinguish: Give the difference between two or more different terms.

1.2.4 Distinguish between the terms empirical formula and molecular formula.

Empirical formula States the elements present in the compound. Simplest whole number ratio of these

elements. Example: Empirical formula of glucose=CH2O

Molecular formula• The elements present in the compound• Actual number of atoms of the elements in one

molecule• Example: Molecular formula of

glucose=C6H12O6

IB Core Objective 1.2.5 Determine the empirical

formula from the percentage composition or from other experimental data.

Determine: Find the only possible answer (Obj. 3)

1.2.5 Determine the empirical formula from the percentage composition or from other experimental data.An analogy

A test is worth 100% and there are 3 sections:

Section A = 20 marks Section B = 50 marks Section C = 30 marks

What % of the test is Section A? What would you make the test out of to make

mark calculations easy? The easiest way to mark this test is to make the total

100.

1.2.5 Determine the empirical formula from the percentage composition or

from other experimental data. You need to determine the empirical formula for a compound of

phosphorous and oxygen that contains 43.64% phosphorus by mass. You are not given a mass, so make up one. Remember, 100 is an easy

number, so let’s start there…. In 100g, there would be 43.64 g of P, and 56.36g of O (100-

43.64=56.36). Now mole it out (find the moles!!) Amount of phosphorus =

= 1.409 mols Amount of oxygen =

= 3.523 molsRatio = 1.409 : 3.523Divide 3.523 by 1.409= 2.5, so 1:2.5. But we need whole numbers!!!!So multiply both sides by two= 2:5 ratio. What is the empirical formula?

1-mol 97.30

64.43

g

g

1-mol g 16.00

56.36g

1.2.5 Determine the empirical formula from the percentage composition or

from other experimental data. Empirical formula with 2:5 ratio would be: P2O5

Finding The Empirical Formula

A compound was found to have a % composition of 38.67 % Carbon 16.22 % Hydrogen 45.11 % Nitrogen

What is the Empirical formula? Click for answer

Answer: CH5N

1.2.5 Determine the empirical formula from the percentage

composition or from other experimental data. You run an experiment where you start with a

compound containing hydrogen and carbon. You use 2.80 g of this compound, and after it

combusts, you have 8.80 g of carbon dioxide and 3.60 g of water.

Use your stoichiometry skills, mole it out, follow the mole ratios, and find the empirical formula.

IB Core Objective 1.2.6 Determine the

molecular formula when given the empirical formula and experimental data.

Determine: Find the only possible answer (Obj. 3)

Molecular Formula Molecular formula is related to the molar

mass of the compound

Sometimes the Molecular Formula is the same as the Empirical Formula.

Ratio = Relative Molecular Mass (Mr)

Empirical Relative Molecular Mass

Multiply the Empirical Formula by the ratio found

Empirical and Molecular Formulas

A compound was found to contain 71.65 % Cl 24.27 % C 4.07 % H The molar mass is known to be 98.96g/mol

What is the empirical and molecular formula?

Remember, assume a 100g sample

IB Core Objective

1.3.1 Deduce chemical equations when all reactants and products are given.

Deduce: Reach a conclusion from the information given.

Tips on Balancing

1) To start, balance all the metals

2) Next balance all the non metals EXCEPT for Oxygen and Hydrogen AND that are not in a complex ion.

3) Next balance all complex ions (you must be able to recognize these!!!)

4) Finally balance Oxygen and Hydrogen, if one of the 2 is in its elemental state balance it last.


You already have practice and knowledge of chemical equations.

Practice balancing these equations:

CH4 + O2 CO2 + H2O

C2H5OH(l) + O2(g) CO2(g) + H2O(g)

(NH4)2Cr2O7(s) Cr2O3(s) + N2(g) + H2O(g)

Balancing Practice CH4 + O2 CO2 + H2O

C2H5OH(l) + O2(g) CO2(g) + H2O(g)

(NH4)2Cr2O7(s) Cr2O3(s) + N2(g) + H2O(g)

Solid lithium hydroxide is used as a carbon dioxide absorber on the space shuttle. The products formed are solid lithium carbonate and liquid water. What mass and volume of carbon dioxide will be absorbed if 1.00kg of lithium hydroxide is used at S.T.P.? (HW)

Don’t forget the State

subscripts!

IB Core Objective 1.3.2 Identify the mole ratio of

any two species in a chemical equation.

Identify: What is the definition? Your turn….

Identify: Find an answer from a given number of possibilities. (Obj 2)

1.3.2 Identify the mole ratio of any two species in a chemical equation.You already have practice with this as well.

Yeahh!Practice makes perfect….

2NaOH(aq) + H2SO4(aq) Na2SO4(aq) + 2H2O (l)

What is the ratio of sodium hydroxide to sodium sulfate?

What is the ratio of sodium hydroxide to sulfuric acid?

What is the ratio of moles of oxygen atoms in sulfuric acid to moles of sulfuric acid?

What is the ratio of moles of oxygen atoms in water to moles of water?

IB Core Objective 1.3.3 Apply the state symbols

(s), (l), (g), and (aq).

Apply: Use an idea, equation, principle, theory, or law in a new situation.

1.3.3 Apply the state symbols (s), (l), (g), and (aq).

(s) = solid(l) = liquid(g) = gas(aq) = aqueous solution

Intermission Dance Party!!!!!!


1.3.3 Apply the state symbols (s), (l), (g), and (aq). For a reaction occurring in aqueous solution forming a precipitate (solid), or part of an acid-base or redox reaction, it is often better to write the ionic equation.

For example: Pb(NO3)2(aq) + 2NaCl(aq) PbCl2(s) + 2NaNO3(aq)

What are the ions which would be in solution (non-solid) for each of these molecules? Write them down.

Then put the ions and solid in an equation, just like above. This is the ionic equation.

1.3.1 Deduce chemical equations when all reactants and products

are given.1.3.3 Apply the state symbols (s),

(l), (g), and (aq). The previous ionic equation is often referred to as

the complete ionic equation. However, we can reduce this to the net ionic equation.

To do this, we get rid of the spectator ions. This would be any ions that are not involved in forming the main product.

Pb2+(aq) + 2NO3

-(aq) + 2Na+

(aq) + 2Cl- (aq)

PbCl2(s) + 2Na+(aq) + 2NO3

-(aq)

Which ones are the spectator ions? (Which appear twice?). Take these out, re-write, and you have the net ionic equation.

1.3.1 Deduce chemical equations when all reactants and products are given.1.3.3 Apply the state symbols (s), (l),

(g), and (aq).Answer

Net ionic equation:Pb2+

(aq) + 2Cl- (aq)

PbCl2(s)

IB Core Objective

1.4.1 Calculate theoretical yield from chemical equations.

Calculate: Find a numerical answer

showing the relevant stages in the working (unless instructed not to do so).

1.4.1 Calculate theoretical yield from chemical equations.

You already have practice doing this with mass to mass calculations!

Practice: What mass of sodium hydrogencarbonate (NaHCO3) must be heated to give 8.80g of carbon dioxide (CO2)?

2NaHCO3 → Na2CO3 + CO2 + H2O

Answer: 33.6 g

IB Core Objective

1.4.2 Determine the limiting reactant and the reactant in excess when quantities of reacting substances are given.

Determine: Find the only possible answer.

1.4.2 Determine the limiting reactant and the reactant in

excess when quantities of reacting substances are given.

We sometimes don’t always have perfect amounts of each reactant.

We can only make as much product as the limiting reactant will allow.

We must determine which reactant is limiting


excess when quantities of reacting substances are given.Finding The Limiting Reactant

1) Balance the chemical equation

2) Find the number of mol’s of each reactant

3) Divide the # of moles by the coefficient found in the balanced equation.

4) The chemical that has the smallest value is the limiting reactant.

1.4.2 Determine the limiting reactant and the reactant in excess when quantities of reacting substances are given.

In the reaction 2NH3 + CO2 → (NH2)2CO + H2O

You have 25.5 g of ammonia (NH3) and 22.0 g of carbon dioxide (CO2).

Which is the limiting reactant? What is the mass of each product? How much reactant is left over?

Answers: Limiting: carbon dioxide Mass of each product: (NH2)2CO = 30.0g H2O =

9.01 g. NH3 left over= 8.52 g


excess when quantities of reacting substances are given.

2.50 g of methane is mixed with 3.00 g of water 1) Which reactant is the limiting one? 2) What is the mass of each product? 3) What is the mass of reactant left?

CH4(g) + H2O(g) CO(g) + H2(g)

IB Core Objective

1.4.3 Solve problems involving theoretical, experimental and percentage yield.



Theoretical yield: Value that you should get mathematically.

Experimental yield: The value you actually get from an experiment.

Percentage yield= x 100% yield lTheoretica

yield alexperimentor Actual


Put it all together: limiting reactants and yield.For the reaction H2O2(aq) + 2KI(aq) + H2SO4(aq) →

I2(s) + K2SO4(aq) + 2H2O(l)

If you add 100.00 g of KI to a solution of 12.00 g of hydrogen peroxide (H2O2) and 50.00 g of sulfuric acid (H2SO4), what would the theoretical yield of iodine (I2) be?

Answer: 76.44 g

In the experiment you performed, you produced an experimental yield of 62.37 g of iodine (I2). What was the percentage yield?

Answer: 81.59%

Question

What is the composition by mass of 1 mol of Iron(III) Oxide? Click for answer:

M = 159.7 g/molFe = 69.9%O = 30.1%

If it doesn’t add up to 100% something is

wrong!

CONCENTRATIONChemical Math

IB Core Objective

1.5.1 Distinguish between the terms solute, solvent, solution and concentration (g dm-3 and mol dm-3)

Distinguish: Give the difference between two or more different items.


Solution: Homogenous mixture of two or more substances.

Solvent: Liquid in which the dispersion occurs.

Solute: The substance dissolved in the solvent.

So….a solution contains a solute dissolved in a solvent.

Concentration: Amount of substance contained within a given volume


Concentration C = Concentration or Molarity (mol/L or

mol/dm3 or M) Molarity = moles of solute

Liters of solvent V = volume (L, dm3)

Q: How many moles are in a 25cm3 of 10M sulphuric acid (H2SO4)?

A: 0.25 moles

IB Core Objective

1.5.2 Solve problems involving concentration, amount of solute and volume of solution.



Q: Calculate the molarity of a solution prepared by dissolving 1.56 g of gaseous HCl in enough water to make 26.8ml(cm3) of solution.

A: 1.60M HCl

Click for answer


Calculate the number of moles of each ion in 1.75L of 1.0 x 10-3 M ZnCl2

A: 1.8*10-3 mol Zn2+

3.5*10-3 mol Cl-

Click for answer


Dilutions Sometimes a concentrated solution will

have solvent added to produce a more dilute one. # of moles does not change so, ‘n’ is common

to both!!!

C1 x V1 = C2 x V2


Q: What volume of 16M sulfuric acid must be used to prepare 1.5L of a 0.10M H2SO4 solution? Click for answer

A: 9.4 *10-3dm3 or 9.4 cm3 (mL)

Special note: Always add acid to water not the other way around!!

The Hindenburg-1937

The Challenger

Shuttle1986

http://upload.wikimedia.org/wikipedia/commons/3/39/Challenger_STS-51-L-launch.jpg

Mistakes in Stoichiometry

1999 Mars Orbital Lander

http://upload.wikimedia.org/wikipedia/commons/1/19/Mars_Climate_Orbiter_2.jpg

IB Core Objective

1.4.4 Apply Avogadro’s law to calculate reacting volumes of gases.

Apply: Use an idea, equation, principle, theory, or law in a new situation.


At a constant temperature and pressure, a given volume of any gas always contains the same number of particles.

In other words, equal amounts of gases at the same temperature and pressure occupy the same volume!


Using the following reaction C2H2(g) + 2H2(g) → C2H6(g)

If you had 10cm3 of ethyne (C2H2), what volume of hydrogen (H2) would you need to fully react with it?

What is the volume of ethane (C2H6) that would be produced?

Answer: 20cm3 H2

10cm3 of ethane

IB Core Objective

1.4.5 Apply the concept of molar volume at standard temperature and pressure in calculations.

Apply: Use an idea, equation, principle, theory or law in a new situation. (Obj. 2)

1.4.5 Apply the concept of molar volume at standard temperature and pressure in

calculations.

Molar volume: The volume of any gas that contains one mole.

If temperature and pressure are specified, then molar volume can be calculated.

At Standard Temperature and Pressure (STP): 1 mol of gas occupies 22.4dm3

0oC = 273.15K, 1atm = 760 mm Hg = 760 torr = 101.3kPa

1.4.5 Apply the concept of molar volume at standard temperature and pressure in

calculations.

How many moles of oxygen (O2) are there in 5.00 dm3 of oxygen?

Answer: 0.223 mol

IB Core Objective

1.4.6 Solve problems involving the relationship between temperature, pressure and volume for a fixed mass of an ideal gas.

Solve: Obtain an answer using algebraic and/or numerical methods. (Obj. 3)

1.4.6 Solve problems involving the relationship between temperature, pressure and volume for a fixed mass of an ideal

gas.

Ideal gas: Particles have negligible volume, there are no attractive forces between particles, and kinetic energy is proportional to absolute temperature.

Boyle’s Law: volume is inversely proportional to pressure at a constant temperature.

i.e. When volume decreases, pressure increases. When volume increases, pressure decreases.

1.4.6 Solve problems involving the relationship between

temperature, pressure and volume for a fixed mass of an ideal gas.

Charles’s Law: Volume is proportional to temperature at constant pressure. (This is for variable volume only, such as a balloon) Therefore, doubling the temperature doubles the volume.

Gay-Lussac’s Law: The pressure is proportional to the absolute temperature of the gas.Therefore, increasing the temperature increases the pressure, and vice versa.How do we put this all together….?

1.4.6 Solve problems involving the relationship between temperature,

pressure and volume for a fixed mass of an ideal gas.

P1V1/T1 = P2V2/T2

The one refers to the initial measurement, the two refers to the second measurement.

If one of the values is constant, then you can just remove that value!

1.4.6 Solve problems involving the relationship between temperature,

pressure and volume for a fixed mass of an ideal gas.

A sample of methane gas that has a volume of 3.8L at 5oC is heated to 86 oC at constant pressure. Calculate its new volume.

Remember to convert Celsius to Kelvins!

Answer: 4.9L

Click for answer

IB Core Objective

Solve problems using the ideal gas equation, PV=nRT

Solve: Obtain an answer using algebraic and/or numerical methods. (Obj. 3)

1.4.7 Solve problems using the ideal gas equation, PV=nRT

Universal Gas Equation: PV=nRT

P = Pressure V = Volume N = # of mols T = Temperature (K) R = Universal Gas Constant = 8.314 JK-1 mol-1

OR =0.08206 (L•atm)(K•mol)-1

1L = 1000cm3

1L = 1dm3

1000cm3 = 1dm3

1.4.7 Solve problems using the ideal gas equation, PV=nRT

A sample of hydrogen gas has a volume of 8.56dm3 at a temperature of 0.00C and a pressure of 152.0 kPa. Calculate the moles of hydrogen gas present in this gas sample

P = V = n = T = R = 0.08206 (L•atm)(K•mol)-1

Or = 8.314 JK-1 mol-1

PV = nRT

Answer: 0.57 mol

Click for answer

IB Core Objective

1.4.8 Analyse graphs relating to the ideal gas equation.

Analyse: Interpret data to reach conclusions. (Obj. 3)

1.4.8 Analyse graphs relating to the ideal gas equation.

Homework: Look at the graphs in your textbook.

Analyse: Would Gay-Lussac’s Law look the same as Boyle’s Law or Charles’s Law?

chemical math. 1.1.1 apply the mole concept to substances. apply: use an idea, equation principle,...

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