Section 1B The Mole Concept & Chemical Calculation/ Page 1
Section 1BThe Mole Concept & Chemical Calculation
Mole and Avogadro Number
Chemists developed a unit to represent the number of particles in a sample. This unit is the mole (Latin, means 'pile').
The mole was defined as the amount of substances which contains the same number of particles as in 12 g of .
Experiments show that 12 g of carbon has 6.02 x 1023 atoms. This number is known as Avogadro number (honoring an Italian chemist, Amadeo Avogadro).
The Mass of One Mole of a Substance
The weight of 1 mole of substance (molar mass) always corresponds to its formula mass express in gram units.
In the definition for mole, the particles may be atoms, molecules, ions, electrons or other particles.
no. of mole = / no. of mole =Example 1A 5 cm3 spoon can hold 1.67 x1023 molecules of water.
a)What is the number of moles of water molecules in the spoon?
b)What is the mass of water in the spoon?
Example21 mole of helium atom weighs ______g and contains ______helium atoms, i.e. ______mole of helium atoms.
1 mole of nitrogen molecules weighs ______g and contains ______moles nitrogen atoms
1 mole of AlCl3 weighs ______g, contains ______mole of aluminium ions and ______moles of chloride ions.
______
.1What is the mass of 2.5 moles of potassium atoms?
2What is the number of nitrogen atoms in 0.5 mole of nitrogen gas, N2?
3The number of sodium atoms in 4.6 g of sodium metal is
4Calculate the mass of
a] 3.0 mole of neon atoms
b] 0.10 mole of lithium atoms
The Molar Volume
The volume occupied by one mole of a substance is called the molar volume.
For gases, experiments show that at the same temperature and pressure, molar volumes of allgases are roughly equal.
Gas / Formula / Molecular mass / Density(g dm-3 ) / Molar volume
(dm3 )
Hydrogen / 0.083
Helium / 0.166
Ammonia / 0.706
Oxygen / 1.333
Carbon dioxide / 1.811
Chlorine / 2.994
i.e. The molar volume of any gas is approximately ______at 25oC 。and 1 atmospheric pressure (r.t.p.)
The molar volume of any gas is ______at standard teperature and pressure (s.t.p.)
Avogadro's Law
Avogadro's law states that equal volumes of all gases at the same temperature and pressure contains the same number of molecules.
For example, 24 dm3 of any gases at r.t.p. contain 1 mole of molecules.
Example 1How many moles of carbon dioxide is present in 5.58 dm3 of this gas at s.t.p. ?
.5What is the number of moles of molecules in 6 dm3 of oxygen gas?
61.4 g of a gas has a volume of 1.2 dm3 at r.t.p. Calculate the relative molecular mass of the gas.
no. of mole =The Ideal Gas Equation
In 1662, Robert Boyle had discovered that the volume of a fixed mass of gas is inversely proportional to its pressure, provided the temperature remains constant. This is known as Boyle's Law, Which can be expressed as:
PV = constantor V
In1787, Charles showed that the volume of a fixed mass of gas is directly proportional to its absolute temperature (0oC = 273K), provided the pressure remains constant. This is called the Charles's Law which can be expressed as:
= constantor V T
In 1811, the Italian scientist Avogadro put forward his theory which stated that equal volumes(V) of gases, under the same conditions of temperature and pressure, contain equal numbers(n) of molecules.
i.e. V n
By considering the above 3 Laws, we can obtain the following result:
V and V T and V n
V PV nT
PV = nRT(The Ideal Gas Equation)R = Universal gas constant
Determination of relative molecular masses
The Ideal Gas Equation provides the basis for the determination of the relative molecular massof a gas or low boiling liquid. By finding the volume of the gas (or vapour formed from a known mass of a liquid), at a known temperature and pressure, the relative molecular mass of the compound can be calculated.
The apparatus and experimental procedure used to determine the relative molecular mass of a volatile substance (e.g. propanone) is given below:
Procedure:
1.The apparatus is set up as shown, with a few cm3 of air being deliberately drawn into the gas syringe. This allow for some space for the propanone to vaporise and expand smoothly in the gas syringe.
2.Pass steam through the jacket until the thermometer reading and the volume of air in the syringe reach steady values. Record the temperature and air volume(V1).
3.Rinse the hypodermic syringe with the liquid that is to be investigated. Recharge the hypodermic syringe with about 1 cm3 of liquid, expel air from the needle by pushing in the plunger gently. Dry the outside of the needle.
4.Inject about 0.2 cm3 of liquid into the large syringe. The volume of liquid injected needs not to be very accurately noted, since the mass of the liquid injected would be determined by weighing the hypodermic syringe before and after injection. Between the weightings handle the hypodermicsyringe as little as possible to reduce loss of liquid by expansion or evaporation.
5.Record the volume(V2) of air plus vapour in the graduated syringe when the reading become steady (this ensures complete vaporization of liquid and the vapour pressure inside is equal to atmosphericpressure outside). Pressure = 1 atm ; Volume of vaporized gas = V2 - V1
______
Example 1Calculate the molar mass of B, given that 0.850 g of B occupied 59.5 cm3 at r.t.p.
.70.228 g of liquid was injected into a gas syringe. The volume of vapour formed was 86.3 cm3 at r.t.p. Calculate the molar mass of the substance.
Dalton's Law of Partial Pressure
Dalton's law of partial pressure states that the total pressure of a mixture of gases which do not react together chemically is equal to the sum of the pressures that each gas would exert if it occupied the space alone.
Ptotal = P1 + P2 + P3 + + Pn
Partial pressure of a gas is the pressure that the gas would exert if it alone occupied the wholevolume. Mathematically, it can be expressed as follow:
Ptotal = / / Partial pressure , P1 =The magnitude of the partial pressure of a gas is related to the number of mole of that gas present in the container:
mole fraction (1) =
/ Partial pressure , P1 =______
Example 1:A mixture of gases at a pressure of 1.01 x 105 Nm-2 contains 25% by volume of oxygen. What is the partial pressure of oxygen in the mixture?
.8A mixture of gases at a pressure 7.50 x 104 Nm-2 has the volume composition 40% N2 ; 35% O2 ; 25% CO2.
(a)What is the partial pressure of each gas?
(b)What will the partial pressures of nitrogen and oxygen be if the carbon dioxide is removed by the introduction of some sodium hydroxide pellets?
Faraday and the mole
Quantity of Electricity
Quantity of electricity (Q) = current (I) X time (t)
in coulombs (C) in amperes (A) in seconds (s)
Example 1 : A current of 0.25 A passing for 2 minutes. What is the quantity of electricity passed ?
The Faraday Unit
1 Faraday = 1 mole of electrons = 96500 coulombs
Example 1:Find the quantity of electricity (in faradays) required to liberate
i)1 mole of Na+
ii)0.5 mole of Fe2+
.9.Find the quantity of electricity (in faradays) required to liberate
i)1 mole of Cu2+
ii)2 moles of Al3+
iii)2 moles of H2
Faraday's Law of Electrolysis
Faraday's First Law
The mass (m) of a substance liberated at an electrode during electrolysis is directly proportional to the quantity of elecltricity (Q) passed through the electrolyte.
i.e.m Q
Faraday's Second Law
The quantity of electricity (Q) required to produce a mole of a substance from its ions is proportional to the charge on the ions (Mn+).
Q n
Example 1: A current of 1.5 A was passing through a solution of silver nitrate for 1.5 hours. What was the mass of silver produced ?
Example 2: How many hours will it take for a current of 1.5 A to deposit 0.80 g of copper from a solution of copper sulphate ?
.10.A metal M has a relative atomic mass of 88. When a current of 0.5A was passed for 16 minutes 5 seconds, 0.22 g of M was deposited on the cathode.
i)Calculate the number of faradays of electricity needed to liberate 1 mole of M atoms.
ii)What is the charge carried by an ion of M ?
iii)Write an ionic equation for the reaction at the cathode.
11.Whan an aqueous solution of sodium hydroxide is electrolysed using platinum electrodes, the hydroxide ions are discharged at the anode to give oxygen according to the following half-equation:
4 OH- (aq) 2 H2O (l) + O2 (g) + 4 e-
If a current of 2.5 A is passed for 15 minutes,
i)how many moles of OH- ions are discharged ?
ii)how many moles of oxygen (O2) are produced ?
iii)what is the volume of this oxygen at r.t.p. ? (molar volume of gases at r.t.p. = 24 dm3 )
12.A metal spoon is electroplated with silver in silver nitrate solution, using a current of 0.5 A for one hour. (relative atomic mass: Ag = 108.0 ; 1 Faraday = 96500 C)
i)Draw a labelled diagram showing how this experiment can be carried out in the laboratory.
ii)Write an equation for the reaction which occurs at the metal spoon.
iii)Calculate the mass of silver deposited on the spoon.
Chemical Formulae
Chemical formulae can sometimes be predicted from the theoretical argument based on the atomic structure, but basically they are determined experimentally.
In order to find the formula of a compound, we should know
a]what elements are present ; and
b]relative number of each atoms/ions present in the compound.
There are several types of formulae which are commonly used. These are:
1. Empirical formula - It is the formula which shows the simplest integral (whole number) ratio of the relative number of atoms or ions present.
2.Molecular formula - It is the formula which shows the actual number of each kind of atom in onemolecule of the compound. (This type of formula is only applicable for covalent compounds because only covalent compounds are exist in discrete molecules)
Determination of formulae of simple compounds from percentage composition by mass
In order to find the formula of a compound, it is first necessary to find the ratio by mass of each element in the compound.
After finding the masses of each element, these masses can be converted into moles. The ratio of these mole values gives the empirical formula.
Example 1: To find the formula of copper oxide
In performing the above experiment, the following points should be noted:
i]It is necessary to pass the town gas for a few seconds before igniting it at the outlet. This is toensure that all the air inside the tube has been displaced. The gas coming out of the hole is thus pure town gas, which will burn quietly and safely on ignition.
ii]Excess town gas has to be burnt away, otherwise it will escape into the laboratory. Town gas is poisonous and may catch fire easily.
iii]The solid residue after complete reaction should be allowed to cool with town gas still passing over it. If the town gas supply is stopped at once after the reaction, air will be drawn into the glass tube as it cools, then the hot copper would easily combine with oxygen in the incoming air to form back copper oxide. To prevent this, copper is allowed to cool in an atmosphere of town gas.
Specimen results:
mass of test tube= 21.320 g
mass of test tube + copper oxide = 22.950 g
mass of test tube + copper= 22.622 g
mass of copper oxide= ______g
mass of copper in oxide= ______g
mass of oxygen in oxide= ______g
(Given: atomic mass of copper= 63.5 ; atomic mass of oxygen = 16)
no. of mole of copper in copper oxide= =
no. of mole of oxygen in copper oxide= =
ratio of Copper(Cu) : Oxygen(O)= ___ : ___
Therefore, the formula of copper oxide is ______.
Example 2: To determine the empirical formula of magnesium oxide
Specimen results:
mass of crucible + lid= 20.635 g
mass of crucible + lid + magnesium = 21.555 g
mass of crucible + lid + magnesium oxide= 22.165 g
mass of magnesium oxide= _____ g
mass of magnesium = _____ g
mass of oxygen present in the oxide= _____ g
Mg / Ono. of mole
ratio
Therefore, the formula of magnesium oxide is ______
Example 3: A compound has the empirical formula CxHy . On analysis, 1.000 g of the compound is found to contain 0.857 g of carbon. Find values of x and y .
C / Hmasses
no. of mole / = / =
ratio
Empirical formula is ______. Therefore , x = ___ and y = ___.
Example 4: A compound X contains 80 % carbon and 20 % hydrogen. Find its empirical formula. Find also its molecular formula if the vapour density of X is 15 .
Assume we have _____ g of compound X.
Carbon / Hydrogenmasses
no. of mole / = / =
ratio
Empirical formula is ______.
Vapour density= =
= =
=
Molecular mass of X = 2 x V.D.==
Let ______be the molecular formula of X.
Molecular formula of X is ______.
13A sample of a hydrated compound was analysed and found to contain 2.10 g of cobalt, 1.14 g of sulphur, 2.28 g of oxygen and 4.50 g of water. Calculate its empirical formula. (CoSO4 . 7 H2O)
Co / S / O / H2Omasses
no. of mole / = / = / = / =
ratio
Empirical formula is ______. (no molecular formula for ionic compound)
1410.00 g of hydrated barium chloride is heated until all the water is driven off. The mass of anhydrous compound is 8.53 g . Determine the value of x in BaCl2 . x H2O. (2)
15Determine the formula of a mineral with the following mass composition: Na = 12.1 % ; Al = 14.2 % ; Si = 22.1 % ; O = 42.1 % ; H2O = 9.48 %. (Na2Al2Si3O10 . 2 H2O)
Calculation based on equations
If the balanced equation for one reaction is known, it is possible to calculate the masses of theproducts if the masses of the reactants are given, or vice versa. The steps in this type of calculation are as follow:
a]write down the balanced equation for the reaction
b]convert the amounts of given substances into mole quantities (this may not be necessary in case of gases reactions)
c]calculate the mole quantities of the required substances using the stoichiometric coefficient given by the equation
d]change the mole quantities back into mass or volume as required by the question
Example 1: Calculate the volume of hydrogen evolved at r.t.p. when 1.3 g of sodium reacts with excess water.
Step 1Equation
Step 2into no. of moles
Step 3moles by equation
Step 4into volume
Example 2: Calculate the mass of magnesium oxide formed when 2.43 g of magnesium are burnt with excess oxygen.
Calculation involving gaseous volume
In this type of calculation, we must first know a very important fact - the Avogadro's Law. This law states that equal volumes of all gases contain the same number of molecules (if temperature and pressure are the same). Therefore, by applying Avogadro's law, mole ratio of gases can be converted into volume ratio and vice versa.
Example 1: Methane, CH4, burns in oxygen to give carbon dioxide and water. If 10 dm3 of methane burns, calculate :
[a] the volume of oxygen required ;
[b] the volume of the products formed (measured at room temperature and pressure).
Equation :
mole by
equation
volume by
Avogadro‘s law
Volume of oxygen= ______
Volume of products ( )= ______
Volume of products ( )= ______
Example 2: Calculate the volume of oxygen required for the complete combustion of 100 cm3 of ethane, C2H6 . What is the volume of carbon dioxide and water formed, assuming all the volumes are measured at room temperature and pressure?
Molarity of a Solution
Molarity (M) is the number of moles of solute dissolved in 1 dm3 of solution.
Molarity of a solution(M) =
Number of moles of solute present = Molarity x Volume of solution in dm3
i.e. n = M x V
______
Example 1How many grams of sodium hydroxide are needed to prepare 3 dm3 of 2M NaOH?
Example 2How many dm3 of 0.05 M NaCl can be prepared from 11.7 g of NaCl ?
______
16Calculate the molarity of each of the following solutions:
a)4 g of NaOH in 1 dm3
b)9.8 g of H2SO4 in 500 cm3
17Calculate the mass of solute in each of the following solutions:
a)250 cm3 of 2M NaOH
b)100 cm3 of 0.5 M HCl
______
Calculations in Acid-Base titrations
Example 120.0 cm3 of a solution of barium hydroxide, Ba(OH)2 , of unknown concentration is placed in a conical flask and titrated with a solution of hydrochloric acid, HCl , which has a concentration of 0.06 M . The volume of acid required is 25.0 cm3 . Calculate the concentration of the barium hydroxide solution.
Step 1Equation
Step 2into moles
Step 3moles by equation
Step 4into concentration (M)
Example 22.65 g of sodium carbonate (Na2CO3) were dissolved in water and made up to 250 cm3 solution. 25.0 cm3 of this required 20.0 cm3 of a hydrochloric acid solution for complete reaction. Find the molarity of the hydrochloric acid.
Step 1Equation
Step 2into moles
Step 3moles by equation
Step 4into molarity (M)
Example 3.50.0 cm3 of 0.50 M nitric acid were added to 1.28 g of a sample of calcium carbonate containing sand as impurity. The excess acid was found to be neutralized by 20.0 cm3 of 0.40 M sodium hydroxide solution. Find the percentage purity of the calcium carbonate.
Step 1Equation 1
Equation 2
Step 2into moles
Step 3moles by equation
Step 4into mass (g)
.18On diluting a sample of ethanoic acid (CH3COOH) five times, it was found that 25 cm3 of the dilute solution required 30.0 cm3 of 0.10 M sodium hydroxide solution for complete neutralization. What was the concentration of original acid in mol dm-3 ? (0.60 M)
Step 1
Step 2
Step 3
Step 4
195.00 g of an impure sample of potassium carbonate (K2CO3) required 34.2 cm3 of 2.00 M hydrochloric acid for complete reaction.
What is the percentage purity of the carbonate?(94.4 %)
Step 1
Step 2
Step 3
Step 4
208.0 g of a sample of hydrated sodium carbonate , Na2CO3 . n H2O , are dissolved in water and the solution is made up to 250 cm3. Using methyl orange as indicator, 25 cm3 of this solution required 28.0 cm3 of 0.10 M sulphuric acid for complete reaction. Calculate n , the number of molecules of water of crystallization, in the sample of sodium carbonate crystals. (10)
Step 1
Step 2
Step 3
Step 4
______
Calculations in Redox Titration
Example 1Acidified potassium permanganate solution oxidizes oxalic acid to carbon dioxide and water according to the following equation:
2 MnO4-(aq) + 5 H2C2O4(aq) + 6 H+(aq) 2 Mn2+(aq) + 10 CO2(g) + 8 H2O(l)
25 cm3 of 0.20 M oxalic acid solution required 20.0 cm3 of potassium permanganate solution for complete reaction. Find the molarity of the potassium permanganate solution.
Step 2
Step 3
Step 4
.21Potassium permengate solution oxidizes iron(II) salt to iron(III) salt according to the following ionic equation:
5 Fe2+(aq) + MnO4- (aq) + 8 H+ (aq) 5 Fe3+ (aq) + Mn2+ (aq) + 4 H2O (l)
1.817 g of potassium permanganate are dissolved in water to give 250.0 cm3 of aqueous solution. 2.185 g of an iron(II) salt are dissolved in water and the solution made up to 100 cm3 . 40.0 cm3 of this iron(II) salt solution require 25.0 cm3 of the permanganate solution for complete reaction.
(a)What is the molarity of the potassium permanganate solution? (0.046 M)
(b)What is the molarity of the Fe2+ ions in the iron(II) salt solution? (0.1438 M)
(c)Given that 1 mole of the iron(II) salt contains 1 mole of Fe2+ ions, what is the molar mass of the iron(II) salt ? (152.0 g)
(d)What is the percentage by mass of iron in the salt ? (36.84%)
2225.0 cm3 of a solution of potassium permanganate(KMnO4) were added to excess of potassium iodide(KI) solution and the iodine(I2) liberated was titrated with sodium thiosulphate(Na2S2O3) solution. 25.2 cm3 of 0.12 M thiosulphate solution were used. Calculate the molarity of the permanganate solution. (0.0242 M)
Equation 1 :
Equation 2 :
no. of mole of S2O32- used=
no. of mole of I2 formed=
no. of mole of I - reacted=
no. of mole of MnO4- used=
Molarity of MnO4- solution=
Past Paper
96IIA2(a) (ii)At 298 K, 1.0 dm3 of N2 at 0.20 Pa pressure was mixed with 2.0 dm3 of O2 at 0.40 Pa in a 4.0 dm3 container. Assuming that both N2 and O2 behave ideally, calculate the pressure of the gaseous mixture at 298 K.
(2 marks)
95IIA3(a)(i)Derive an expression for the molar mass M of an ideal gas, in terms of its density d, pressure P, and absolute temperature T.
(ii)At 98.6 kPa and 300 K, the density of a sample of dry air is 1.146 g dm- 3. Assuming that dry air contains only nitrogen and oxygen and behaves ideally, calculate the composition of the sample.
(Gas constant, R = 8.31 J K- 1 mol- 1)(5 marks)
94IA1(d)An aqueous solution of a titanium (Ti) salt was electrolysed by passing a current of 5.00 A for 2.50 hours. As a result, 5.60 g of metallic Ti were deposited at the cathode. Deduce the charge on the Ti ion in the solution.
(Given: 1 faraday = 96500 C mol- 1)(3 marks)
91IA2(c)A container holds a gaseous mixture of nitrogen and propane. The pressure in the container at 200is 4.5 atm. At - 40oC the propane completely condenses and the pressure drops to 1.5 atm. Calculate the mole fraction of propane in the original gaseous mixture.
(3 marks)
Making Scheme
96IIA2(a)(ii)PV= nRT
0.2(1)= RTand0.4(2)= RT Ptotal (4) = (+)RT