ATOMS, MOLECULES & STOICHIOMETRY

PHYSICAL CHEMISTRY, AS-LEVEL

Content

Relative masses of atoms & molecules

The mole, the Avogadro constant

The determination of relative atomic mass, Ar, & relative molecular mass, Mr, from the mass spectra

The calculation of empirical & molecular formula

Reacting masses & volumes (of solutions & gases)

Things you should be ableto do (part 1)

define the terms ‘relative atomic, isotopic, molecular & formula masses, based on the 12C scale

define the term ‘mole’ in terms of the Avogadro constant

calculate the relative atomic mass of an element given the relative abundances of its isotopes, or its mass spectrum

Topic 6 in IGCSE study guide: Stoichiometry

Relative atomic mass (Ar): the ratio of the average mass of atoms of an element to 1/12 of the mass of atom carbon-12

IUPAC’s definition: An atomic weight (relative atomic mass) of an element from a specified source is the ratio of the average mass per atom of the element to 1/12 of the mass of an atom of 12C.

Questions

What ratio?

Average of what?

Why 1/12 of 12C?

Why carbon-12? It was originally 16O (search in http://www.madsci.org)

ExerciseThe atomic mass scale gives masses in atomic mass units (amu) relative to the mass of carbon-12.

(a) What is the mass of one 12C atom in amu? ____________(b) What is the mass of an average C atom in amu? (abundance: 98.9% 12C & 1.1% 13C) ____________(c) What is the mass of an average Cl atom in amu?(abundance: 75.77% 35Cl & 24.23% 37Cl) ____________(d) What is the mass of an average Br atom in amu? (abundance: 50.69% 79Br & 49.31% 81Br)___________

By definition, 1 amu = 1/12 mass of 12C (which is, by definition = 12.000)

Topic 6 in IGCSE study guide: Stoichiometry (cont’d)

Relative molecular mass (Mr): the sum of the relative atomic masses of all the elements shown in the formula

Mole: the amount of substance of a system that contains as many "elemental entities" (e.g., atoms, molecules, ions, electrons) as there are atoms in 12 g of carbon-12.

1 mole of particle = 6.022 x 1023 items

Exercise2. The molar mass scale gives masses in grams (g) relative to the mass of 12C.

(a) What is the mass in grams of 1 mole (mol) of 12C? ___________(b) What is the mass in grams of 1 mole (mol) of carbon? ___________(c) What is the mass in grams of 1 mole (mol) of Cl? ___________(d) What is the mass in grams of 1 mole (mol) of Na? ___________

3. How many 12C atoms are present in a mole of 12C ?

Things you should be ableto do (part 2)

Define the terms ‘empirical’ and ‘molecular’ formulae

Calculate empirical and molecular formulae, using combustion data or composition by mass

Topic 6 in IGCSE study guide: Stoichiometry (cont’d)

Empirical formula: the simplest ratio of atoms present

Molecular formula: the number of atoms of each element present in one molecule of the substance

Relative is just a number based on the carbon-12 relative atomic mass scale. Molar mass is a term used to describe the mass of one mole i.e. the relative atomic/formula/molecular mass in grams (g).

1 mole of ammonia, NH3, consists of 1 mole of nitrogen atoms combined with 3 moles of hydrogen atoms.

1 mole of aluminium oxide, Al2O3, consists of 2 moles of aluminium atoms combined with 3 moles of oxygen atoms

Exercise

4. Cinnamic alcohol is used mainly in perfumery, particularly in soaps and cosmetics. Its molecular formula is C9H10O.

(a) Calculate the percent composition by mass of C, H, and O in cinnamic alcohol.

(b) How many molecules of cinnamic alcohol are contained in a sample of mass 0.469 g?

Exercise 5. It is found that 207 g of lead combined with 32 g of sulphur

to form 239 g of lead sulphide. From the data work out the formula of lead sulphide. (Relative atomic masses: Pb = 207 and S = 32)

6. It is found that 207 g of lead combined with oxygen to form 239 g of a lead oxide. From the data work out the formula of the lead oxide. (Relative atomic masses: Pb = 207 and O = 16)

7. It is found that 54 g of aluminium forms 150 g of aluminium sulphide. Work out the formula of aluminium sulphide. (Relative atomic masses: Al = 27 and S = 32).

Things you should be ableto do (part 3)

• Write and/or construct balanced equations.

• Perform calculations, including use of the mole concept, involving: (*)

(i) reacting masses (from formulae and equations)

(ii) volumes of gases (e.g. in the burning of hydrocarbons)

(iii) volumes and concentrations of solutions

• Deduce stoichiometric relationships from calculations such as those in (*)

(1) mole of Z = g of Z / atomic or formula mass of Z,

(2) or g of Z = mole of Z x atomic or formula mass of Z

(3) or atomic or formula mass of Z = g of Z / mole of Z

where Z represents atoms, molecules or formula of the particular element or compound defined in the question.

Exercise 8. How many moles of potassium ions and bromide

ions in 0.25 moles of potassium bromide?

9. How many moles of calcium ions and chloride ions in 2.5 moles of calcium chloride?

10. How many moles of lead and oxygen atoms are needed to make 5 moles of lead dioxide?

11. How many moles of aluminium ions and sulphate ions in 2 moles of aluminium sulphate?

Exercise 12. How many moles of chlorine gas in 6.5 g? Ar(Cl)

= 35.5)

13. How many grams of propane C3H8 are there in 0.21 moles of it? (C = 12, H = 1)

14. What mass and moles of magnesium chloride is formed when 5 g of magnesium oxide is dissolved in excess hydrochloric acid?

15. What mass and moles of sodium chloride is formed when 21.2 g of sodium carbonate is reacted with excess dilute hydrochloric acid?

A solution of hydrochloric contained 3.65 g/dm3. A solution of a metal hydroxide of formula MOH was prepared by dissolving 5.0g of MOH in 1 dm3 of water (M is an unknown metal). 25 cm3 of the MOH solution required 22.3 cm3 of the HCl acid solution to neutralise it in a titration procedure using a pipette (MOH) and burette (HCl).The equation for the neutralisation reaction is: MOH + HCl ==> MCl + H2O

Atomic masses: H = 1, Cl = 35.5, O = 16, M = ?

(a) Calculate the mass of MOH neutralised in each titration.(b) Calculate the mass of HCl reacting in each titration.(c) Calculate the formula mass of HCl(d) Calculate the mass of MOH that reacts with 36.5 g HCl and hence the formula mass of MOH.(e) If the metal is in the Group 1 of Alkali Metals, what is the atomic mass of M and what metal is M?

More definitions

Relative isotopic mass: the mass of one atom of the isotope, relative to 1/12 times the mass of one atom of carbon-12 [vs. relative atomic mass definition which uses ‘average’]

Relative formula mass: the mass of one formula unit of the compound relative to 1/12 times the mass of one atom of carbon-12

Proton number, nucleon number, isotopes

Moles of gases In reactions involving gases, VOLUME of the gases is usually

more important than the mass of the gases involved.

Avogadro’s law: under the same conditions of temperature and pressure, equal volume of gases contain equal number of moles

Volume ~ number of moles

Standard conditions: T: 273 K, P: 101 kPa, C:1 mol dm-3.

1 mol of all gases under standard T & P occupy a volume of 22.4 dm3, known as MOLAR VOLUME (Vm). Under room conditions, gas’ molar volume is 24.0 dm3

1. A water sample consists of the isotopes 1H, 2H and 16O.

Write the formula for the different H2O molecules that are present.

Which molecule is the heaviest?

2. Write down the empirical formulae of the following: hexane, hydrogen peroxide

3. An oxide of copper has the following composition by mass: Cu, 0.635 g; O, 0.080 g. Calculate the empirical formula of the oxide

Exercise:Empirical & molecular formula

Exercise:Empirical & molecular formula

4. On complete combustion of 0.400 g of a hydrocarbon, 1.257 g of carbon dioxide and 0.514 g of water were produced.

Calculate the empirical formula of the hydrocarbon

If the relative molecular mass of the hydrocarbon is 84, what is its molecular formula?

5. Write the molecular formula for each compound: a. magnesium bromide, b. hydrogen iodide, c. calcium sulphide, d. sodium sulphate, e. potassium nitrate, f. nitrogen dioxide

6. Name each of the following compounds: a. K2CO3, b. Al2S3, c. LiNO3, d. Ca3(PO4)2, e. SiO2

Exercise:Balancing equations

7. Balance the equations for the following reactions:

a. The thermite reaction: Al + Fe2O3 → Al2O3 + Fe

b. Petrol contains octane. Complete combustion in oxygen produces only carbon dioxide and water.

c. Lead nitrate decomposes on heating to produce PbO, NO2, and O2.

8. Balance the following ionic equations:

a. Cl2(aq) + Br-(aq) → Cl-(aq) + Br2(aq)

b. Fe3+(aq) + OH-(aq) → Fe(OH)3(s)

9. Calculate the amount in moles of nitric acid in 25.0 cm3 of a 0.1 mol dm-3 aqueous solution.

10. Calculate the concentration in mol dm-3 of a solution comprising 0.125 mol of nitric acid with water added, up to a volume of 50 cm3.

11. What is the concentration in g dm-3 of 0.50 mol dm-3 aqueous ethanoic acid (CH3COOH)

12. What is the concentration in mol dm-3 of an aqueous solution containing 4.00 g dm-3 of sodium hydroxide?

Exercise:Concentrations & gas volumes

13. 20.0cm3 of 0.100 mol dm-3 potassium hydroxide exactly neutralises a 25.0 cm3 sample of hydrochloric acid. What is the concentration of the hydrochloric acid in a. mol dm-3 b. g dm-3 ?

14. Determine the stoichiometric ratio, and hence the balanced equation, for the reaction of an insoluble iron hydroxide with dilute nitric acid, HNO3. 4.00 x 10-4 mol of the iron hydroxide is exactly neutralised by 24.0 cm3 of 0.05 mol dm-3 nitric acid.

Exercise:Concentrations & gas volumes

Mass spectrometry

Things you should be ableto do (part 4)

Analyse mass spectra in terms of isotopic abundances and molecular fragments (bold: A2 only)

Mass spectrometer