Calderside Academy Calculations In Higher Chemistry number of moles of each ... How many neutrons are present in 1.6g of oxygen gas? ... 96,500C = 1 Faraday = charge carried by 1 mole

Calderside Academy

Calculations

In

Higher

Chemistry

1

Calculations involving Excess All reactants are needed for a chemical reaction to occur. As soon as one of the

reactants is used up the reaction will stop. Any of the other reactant which is

left is said to be “in excess”.

It is the reactant which is totally used up which determines the mass of

product formed.

Worked example

What mass of carbon dioxide is formed when 8g of methane is reacted with

128g of oxygen?

(1)Find out which reactant is in excess.

Write a balanced equation CH4 + 2O2 CO2 + 2H2O

Mole ratio 1 mol 2 mol

Calculate number of moles of each

reactant present 8/16 128/32

0.5 4

1 mol needs 2 mol

0.5mol needs 1mol

got 4 mol

therefore oxygen is in excess

(2)Work out mass of product.

Write a balanced equation CH4 + 2O2 CO2 + 2H2O

(ignore O2 as it is in excess)

Mole ratio 1 mol 1 mol

Change to mass (or other units 16g 44g

if required)

Use proportion 8g 8 x 44

16

= 22g

Examples for practice 1. What mass of magnesium oxide is produced when 2.4 g of magnesium is burned in 0.5

moles of oxygen?

2 Mg + O2 2 MgO

2. What mass of hydrogen gas is produced when 1.2g of magnesium is added to 500cm3 of

hydrochloric acid, concentration 1 moll-1

Mg + 2HCl MgCl2 + H2

3. What volume of carbon dioxide is produced when 3g of carbon are burned in 0.32g of

oxygen? (Take the molar volume of carbon dioxide to be 24 lmol-1)

2

Percentage Yield Calculations

Percentage yield = actual yield x 100

theoretical yield

The actual yield is given in the question.

The theoretical yield is calculated using a balanced equation.

Worked example

In a reaction 330 kg of carbon dioxide was produced when 120 kg of carbon was

burned. Calculate the percentage yield.

Find theoretical yield using the balanced equation

C + O2 CO2

12g 44g

12kg 44kg

120kg 440 kg

Calculate percentage yield

Actual yield x 100 = 330 x 100 = 75%

Theoretical yield 440

Examples for Practice 1. 10.2g of 1,2-dibromopropane (C3H6Br2) was obtained from 2.6g of propene (C3H6).

C3H6 + Br2 C3H6Br2

Calculate the percentage yield.

2. 1g of hydrogen reacts with excess nitrogen to produce 5g of ammonia.

N2 + 3H2 2NH3


3. Under test conditions 1 tonne of sulphur dioxide reacts with excess oxygen to produce

0.8 tonnes of sulphur trioxide.

2SO2 + O2 2SO3


3

Enthalpy of Combustion

Enthalpy of combustion of a substance is the energy released when one mole of

that substance burns in excess oxygen.

Enthalpy of combustion is exothermic.

Worked Example (Note: the method for all calculations is not always identical)

0.22g of propane, C3H8, is burned to heat 250 ml of water from 22oC to 32oC.

Calculate the enthalpy of combustion of propane.

Use H = cmT H = cmT

(Remember to make = 4.18 x 0.25 x 10

sure mass of water = 10.45

is in kg)

Use proportion 0.22g 10.45kJ

(mass of 1 mole of propane) 44g 44 x 10.45

0.22

= 2090 kJmol-1

Remember the sign Enthalpy of combustion is exothermic so we need a

negative sign

Enthalpy of combustion of propane is -2090kJmol-1

Examples for Practice

1. A gas burner containing butane, C4H10, is used to heat 0.15kg of water from

22.5oC to 31oC. 0.35g of butane is used during the experiment. Calculate

the enthalpy of combustion of butane

2. A can containing 100 cm3 of water at 21oC is heated to 29oC when a burner

containing an alcohol is lit underneath it. If 0.02 mol of the alcohol is

burned in the process, calculate the enthalpy of combustion.

3. A Bunsen burner uses methane, CH4, which has an enthalpy of combustion

of -882kJmol-1. If 0.4g of methane was completely burned to heat a can

containing 500cm3 of water, what would be the maximum temperature rise

which would be produced?

4

Enthalpy of Neutralisation

Enthalpy of neutralisation is the energy released when one mole water is

formed in the neutralisation of an acid with an alkali.

Enthalpy of neutralisation is exothermic.

Worked Example (Note: the method is not always identical)

50cm3 of 1 moll-1 hydrochloric acid, HCl, is mixed with 50cm3 of 1 moll-1

potassium hydroxide, KOH, both at 20oC. The temperature of the resulting

solution rises to 26.9oC. Calculate the enthalpy of neutralisation.

Equation NaOH + HCl NaCl + H2O

Use H = cmT H = cmT

(Remember to add = 4.18 x 0.1 x 6.9

the volume of acid & alkali = 2.88 kJ

and make sure it is in kg)

Find number of moles of water formed n = CV(l) = 1 x 0.05

= 0.05 mol

Use proportion 0.05 mol 2.88kJ

1 mole 1 x 2.88

0.05

= 57.6 kJmol-1

Remember the sign Enthalpy of neutralisation is exothermic so we need

a negative sign.

Enthalpy of neutralisation is - 57.6 kJmol-1


1. 80cm3 of 0.5 moll-1 sodium hydroxide solution, NaOH, and 80cm3 of 0.5

moll-1 hydrochloric acid,HCl, were mixed and a temperature rise of 3.4oC

was recorded. Calculate the enthalpy of neutralisation.

2. 25cm3 of 1 moll-1 H2SO4 is neutralised by 50cm3 of 1 moll-1 KOH. A

temperature rise of 9.1oC is noted. Find the enthalpy of neutralisation.

3. 50cm3 of 0.2 moll-1 NaOH is neutralised by 50cm3 of 0.2 moll-1 HCl.

Calculate the resulting temperature rise. (Take the enthalpy of

neutralisation to be -57.3kJmol-1.)

5

Enthalpy of Solution

Enthalpy of solution of a substance is the energy change when one mole of that

substance dissolves in excess water.

Enthalpy of solution may be exothermic or endothermic.

Worked Example (Note: the method is not always identical)

4g of ammonium nitrate, NH4NO3, is dissolved completely in 100cm3 water in an

insulated container. The temperature of the water falls from 19oC to 16oC.

Calculate the enthalpy of solution of ammonium nitrate.

Use H = cmT H = cmT

(Remember to make = 4.18 x 0.1 x 3

sure mass of water = 1.254 kJ

is in kg)

Use proportion 4g 1.254kJ

(find the mass of 1 mole of NH4NO3) 80g 80 x 1.254

4

= 25.08 kJmol-1

Remember the sign Enthalpy of solution may be exothermic or

endothermic.

The temperature decreased, so the reaction is

endothermic.

Enthalpy of solution of ammonium nitrate is + 25.08 kJmol-1


1. 14.9g of potassium chloride, KCl, is dissolved in 0.2kg of water. The

temperature falls from 22.5oC to 18.5oC. Calculate the enthalpy of solution

of potassium chloride.

2. 0.05 mol of a compound is dissolved in 500cm3 of water causing the

temperature to rise from 19oC to 21oC. Find the enthalpy of solution.

3. The enthalpy of solution of ammonium chloride, NH4Cl, is +15.0kJmol-1.

What mass of ammonium chloride would require to be dissolved to

decrease the temperature of 200cm3 of water by 4oC?

6

Avogadro and the Mole

Avogadro’s constant is the number of elementary particles in one mole of the

substance. It has the value 6.02 x 1023.

Worked example

Calculate the number of atoms in 880g of carbon dioxide.

identify the elementary particle carbon dioxide exists as molecules

1 mole 6.02 x 1023 molecules

44g 6.02 x 1023 molecules

880g 880 x 6.02 x 1023

44

= 1.204 x 1025 molecules

1 carbon dioxide molecule (CO2) has 3 atoms

1 molecule 3 atoms

1.204 x 1023 3 x 1.204 x 1023

= 3.612 x 1023 atoms


1. How many ions are present in 2.25 moles of sulphuric acid, H2SO4?

2. How many neutrons are present in 1.6g of oxygen gas?

3. A sample of ethane, C2H6, contains 2.408 x 1024 atoms of carbon. What

mass of ethane is present?

7

Faraday The quantity of electrical charge flowing in a circuit is related to the current

and the time.

Q = I x t

Where Q is the electrical charge in coulombs (C)

I is the current in amps (A)

t is the time in seconds (s)

96,500C = 1 Faraday = charge carried by 1 mole of electrons

n x F coulombs are required to deposit 1 mole of a substance

where n is the charge on the ion

F is the Faraday (96,500C)

Worked example (Note: the method is not always identical)

What mass of nickel is deposited in the electrolysis of nickel(II)sulphate

solution if a current of 0.4A is passed for 2 hours?

Q = It = 0.4 x (2 x 60 x 60) = 2880C

Ion electron equation Ni2+ + 2 e Ni

nF 1 mole 2 x 96,500 C 1 mole

193,000 C 1 mole

193,000 C 59 g

2880 C 2880 x 59

193,000

= 0.88g


1. In the electrolysis of copper(II)sulphate, a current of 0.1A flowed for 60

minutes. Calculate the mass of copper deposited.

2. Electrolysis of silver(I)nitrate produced 1.08 g of silver per hour. What

current was flowing?

3. A vanadium compound was electrolysed using a current of 0.15A for 45

minutes, during which 0.0534g of vanadium was deposited. Calculate the

charge on the vanadium ion.

8

Hess’s Law Hess’s Law states that the enthalpy change for a chemical reaction depends

only on the enthalpies of the reactants and products and is independent of the

route taken for the reaction.

Worked example Calculate H for the following reaction.

C(s) + 2H2(g) CH4(g)

Using

(1) C(s) + O2 CO2(g) H = -394 kJmol-1

(2) H2(g) + ½ O2(g) H2O(l) H = -286 kJmol-1

(3) CH4(g) + 2O2(g) CO2(g) + 2H2O(l) H = -882 kJmol-1

Rearrange equations to try to get equation we want.

(1) C(s) + O2 CO2(g) H = -394 kJmol-1

(2) x 2 2 H2(g) + O2(g) 2 H2O(l) H = -572 kJmol-1

(3) rev CO2(g) + 2H2O(l) CH4(g) + 2O2(g) H = +882 kJmol-1

Equations should cancel out to give equation we want

C(s) + 2H2(g) CH4(g) H = -84 kJmol-1


1. Calculate H for the following reaction. 2C(s) + 3H2(g) C2H6(g)

Using

(1) C(s) + O2 CO2(g) H = -394 kJmol-1

(2) H2(g) + ½ O2(g) H2O(l) H = -286 kJmol-1

(3) C2H6(g) + 3½ O2(g) 2CO2(g) + 3H2O(l) H = -1542 kJmol-1

2. Calculate H for the following reaction.

2C(s) + 3H2(g) + ½ O2 C2H5OH(g)

Use enthalpies of combustion of carbon, hydrogen and ethanol in the

databook.

3. Calculate H for the following reaction.

2CH4(g) C2H2(g) + 3H2(g)

Use enthalpies of combustion of methane, hydrogen and ethyne, C2H2, in

the databook.

9

Molar Volume Molar volume is the volume occupied by 1 mole of a gas under certain conditions.

Worked example (Note: the method is not always identical)

Under certain conditions carbon monoxide has a density of 0.8 gl-1. Find the

molar volume under these conditions.

0.8 g occupies 1 litre

(mass of 1 mole of CO) 28 g occupies 28 x 1

0.8

= 35 litres


1. Under certain conditions, neon has a density of 0.9 gl-1. Calculate the molar

volume under these conditions.

2. A gas has a molar volume of 29.1 l mol-1 and a density of 2.2 gl-1. Calculate

the molecular mass of the gas.

3. From the data below, calculate the formula mass of gas X.

Mass of empty plastic bottle = 112.80 g

Mass of plastic bottle + X = 113.52 g

Capacity of plastic bottle = 1 litre

Molar volume of gas X = 23.6 litres

10

Reacting Volumes Since 1 mole of any gas occupies the same volume under the same conditions, we

can use a balanced equation to calculate the volume of gases.

Worked example

What volume of carbon dioxide would be produced if 20cm3 of ethane is burned

in excess oxygen?

Write a balanced equation C2H6 + 3½O2 2CO2 + 3H2O

Mole ratio 1 mol 2 mols

Volume statements 1 vol 2 vols

Use proportion 20 cm3 2 x 20

1

= 40cm3

Remember – water is a gas if temperatures are above 100oC


1. 20 litres of propane is burned in 140 litres of oxygen. Calculate the volume

and composition of the resulting gas mixture. (All measurements made at

room temperature.)

2. Hexane reacts with steam (H2O) to form carbon dioxide and hydrogen.

Under certain conditions 4 x 104 litres of hexane is reacted with excess

steam. Assuming the reaction goes to completion, calculate the volume of

(a) carbon dioxide and (b) hydrogen produced.

3. 100 litres of hydrazine, N2H4, is burned in 400 litres of oxygen to form

nitrogen gas and water. What will be the volume and composition of the

resulting gas mixture if all measurements are made at (a) 20oC and (b)

300oC?

11

Calculations from Equations A balanced equation shows the number of moles of each reactant and product

involved in the reaction. This allows us to find the number of moles of a

substance reacting or being produced.

Alternatively, number of moles can be converted into

mass

number of molecules/atoms

volume (for gases, given the molar volume)

etc

Worked example

What mass of carbon dioxide would be produced if 3 g of ethane is burned in

excess oxygen?

Write a balanced equation C2H6 + 3½O2 2CO2 + 3H2O

Mole ratio 1 mol 2 mols

Change moles to units required 30 g 88 g

Use proportion 3 g 3 x 88

30

= 8.8 g

Examples for Practice (Note: the method is not always identical)

All examples refer to the following equation:

Na2CO3 + H2SO4 Na2SO4 + CO2 + H2O

1. When 5.3g of sodium carbonate react with excess acid:

(a) what mass of water is formed?

(b) how many water molecules will be formed?

(c) what volume of carbon dioxide will be formed (Take the molar volume

of carbon dioxide as 22 l mol-1)

2. When excess sodium carbonate is added to 250 cm3 of 2 moll-1 sulphuric

acid:

(a) how many moles of sodium sulphate are formed?

(b) what mass of sodium sulphate is formed

(c) how many sodium ions are formed?

12

pH and Concentration

pH is related to the concentration of hydrogen ions.

e.g [H+] = 1 x 10-1 moll-1, pH = 1

[H+] = 1 x 10-5 mol-1, pH = 5

Also, in aqueous solutions [H+] [OH-] = 10-14 mol2l-2

Worked example

What is the concentration of OH- ions in a solution with pH 9

pH = 9

[H+] = 1 x 10-9

[H+] [OH-] = 10-14, therefore [OH-] = 1 x 10-5

Examples for Practice (Note: the method is not always identical)

1. The concentration of H+ ions is 1 x10-3 moll-1. What is the pH of the

solution?

2. The concentration of OH- is 1 x10-5 moll-1. What is the pH of the solution?

3. The concentration of H+ is 1 x 10-6 moll-1. What is the concentration of

OH-?

4. The concentration of H+ is 2 x 10-6. What is the concentration of OH- ions?

5. The concentration of H+ is 2 x 10-6.

The pH of the solution will be between which two numbers?

13

Radioactivity and Halflife Half-life is the time taken for half of a radioisotope to decay. This value is

constant for that particular isotope.

Usually questions about radioactivity involve

half-life

the time over which the radioactivity has been measured

the quantity or intensity of the radiation

Worked example

A radioisotope has a half-life of 3 days. What fraction of the original isotope

will be present after 12 days?

Original quantity (whole amount) 1

After 1 half-life (3 days) 0.5 (1/2)

After 2 half-lives (6 days) 0.25 (1/4)




1. Po-210 has a half-life of 140 days and decays by alpha emission to give a

stable isotope.

(a) What mass of a 4.2g sample of Po-210 will remain unchanged after

280 days?

(b) What mass will have decayed?

(c) How many atoms will have decayed?

2. A sample of ancient wood is found to have a radioactive count rate due to

carbon-14 of 12 counts min-1. A sample of modern wood has a count rate of

48 counts min-1. Calculate the age of the wood, taking the half-life of

carbon-14 to be 5570 years.

14

Redox Titration Redox titrations are used to find out information about one reactant, using

known information about another reactant.

Worked example

Iron(II)sulphate can be oxidised by potassium dichromate. Calculate the mass

of iron(II)sulphate which will react completely with 500cm3 of dichromate

solution, concentration 0.4 moll-1.

Write a balanced redox equation

6 Fe2+ + Cr2O72- + 14H+ 6Fe3+ + 2Cr3+ + 7H2O

Calculate number of moles of ‘known’ reactant

N = C x V = 0.4 x 0.5 = 0.2 moles Cr2O72-

Use mole ratio to work out number of moles of ‘unknown’ reactant 6

6 Fe2+ + Cr2O72-

6 moles 1 mole

0.2 x 6 0.2

1

= 1.2 mol

Change moles into information required

1 mole of FeSO4 contains 1 mole of Fe2+

therefore, we have 1.2 moles of FeSO4

1 mole of FeSO4 weighs 152 g

1.2 moles weighs 182.4 g

Example for Practice

The chlorine level in a swimming pool was found by titrating samples of water

against iron(II)sulphate .

Cl2 + 2Fe2+ 2Cl- + 2Fe3+

A 50cm3 sample of water from a swimming pool required 12.5 cm3 of

iron(II)sulphate, concentration 2.95 moll-1, to reach the end-point. Calculate the

chlorine concentration in the swimming pool,

(a) in mol l-1 (b) in g l-1

15

Answers

Calculations involving Excess

1. oxygen in excess 4g of magnesium oxide

2. hydrochloric acid in excess 0.1g of hydrogen

3. carbon in excess 0.24 litres of carbon dioxide

Percentage Yield Calculations

1. 81.6%

2. 88.2%

3. 64%

Enthalpy of Combustion

1. -883.3 kJmol-1

2. -167.2kJmol-1

3. 10.55oC

Enthalpy of Neutralisation

1. -56.75kJmol-1

2. -57kJmol-1

3. 1.37oC

Enthalpy of Solution

1. +16.7kJmol-1

2. -83.6kJmol-1

3. 11.9g

Avogadro and The Mole

1. 4.06 x 1024

2. 2.408 x 1023

3. 60g

Faraday

1. 0.118g

2. 0.268A

3. 4+

16

Hess’s Law

1. -104kJmol-1

2. -279 kJmol-1

3. +376 kJmol-1

Molar Volume

1. 22.2 litres

2. 64g

3. 16.99g

Reacting Volumes

1. 60 litres of carbon dioxide, 40 litres of oxygen left over

2. (a) 2.4 x 105 litres (b) 7.6 x 105 litres

3. (a) 300 litres excess oxygen, 100 litres nitrogen

(b) 300 litres excess oxygen, 100 litres nitrogen, 200 litres water (steam)

Calculations from Equations

1. (a) 0.9g (b) 3.01 x 1022 (c) 1.1 litres

2. (a) 0.5 mol (b) 71g (c) 6.02 x 1023

pH and Concentration

1. 3

2. 9

3. 1 x 10-8 moll-1

4. 5 x 10-9 moll-1

5. between 5 and 6

Radioactivity and Halflife

1. (a) 1.05g (b) 3.15g (c) 9.03 x 1021 atoms

2. 11140 years

Redox Titration

(a) 0.369 moll-1

(b) 26.2 gl-1

Documents

Calderside Academy Calculations In Higher Chemistry number of moles of each ... How many neutrons are present in 1.6g of oxygen gas? ... 96,500C = 1 Faraday = charge carried by 1 mole