WAEC SSCE - Chemistry - 1999

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The chemical formula for 2-methylpropane is C₄H₁₀, which means it has four carbon atoms. Therefore, the answer is 4.

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Fluorine (F₂) is the most reactive of the halogens. This is because of its small atomic size and high electronegativity, which allows it to attract electrons easily and form strong bonds with other elements. Additionally, the F-F bond is very weak, which means that it is relatively easy to break and form new compounds. As a result, fluorine reacts vigorously with most other elements, including metals and non-metals.

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Calcium chloride is a deliquescent salt, which means it can absorb moisture from the air and turn into a liquid. This property makes it useful as a drying agent because it can remove moisture from the surroundings and keep the environment dry. When calcium chloride is added to a container with a moist substance, it absorbs the moisture and forms a liquid solution. This makes it effective in preventing the formation of rust, as well as in the drying of gases and solvents. Therefore, the correct answer is "deliquescent".

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The number of effective collisions of molecules of the reactants decreases as the volume of the system is increased. As the volume of the system increases, the space available for the molecules to collide with each other decreases. This leads to a decrease in the frequency of collisions, which in turn decreases the number of effective collisions. Effective collisions are those collisions between reactant molecules that have enough energy and correct orientation to lead to the formation of products. When the volume of the system is increased, the number of collisions decreases, and therefore the number of effective collisions also decreases.

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Calcium atom has 20 electrons in its outermost shell. To attain stability, it needs to lose these electrons. Thus, calcium atom ionizes by losing two electrons to form a calcium ion with a 2+ charge. Therefore, the correct option is "losing two electrons."

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The balanced chemical equation is: Zn(s) + 2HCl(aq) → ZnCl2(aq) + H2(g) First, we need to find the moles of zinc present: m(Zn) = 2.60 g M(Zn) = 65 g/mol (molar mass of Zn) n(Zn) = m(Zn) / M(Zn) n(Zn) = 2.60 g / 65 g/mol n(Zn) = 0.04 mol According to the balanced equation, 1 mole of zinc reacts with 2 moles of hydrochloric acid to produce 1 mole of hydrogen gas. Since we have an excess of hydrochloric acid, all the zinc will react, and the amount of hydrogen produced can be calculated as follows: n(H2) = n(Zn) × 1 mol H2 / 1 mol Zn n(H2) = 0.04 mol Now we can use the ideal gas law to find the volume of hydrogen produced at STP: PV = nRT where P is the pressure (which is 1 atm at STP), V is the volume, n is the number of moles, R is the gas constant (0.08206 L·atm/mol·K), and T is the temperature (273 K at STP). Solving for V: V = nRT / P V = (0.04 mol) × (0.08206 L·atm/mol·K) × (273 K) / (1 atm) V = 0.89 L V = 0.89 dm3 (since 1 L = 1 dm3) Therefore, the volume of hydrogen produced at STP is 0.89 dm3, which is option (B).

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Helium is preferred to hydrogen in filling balloons because hydrogen is inflammable. This means that if a balloon filled with hydrogen comes in contact with a flame or spark, it can easily catch fire and explode. On the other hand, helium is non-flammable, making it a safer option for filling balloons.

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The elements that loss electrons most readily are located in Group 1A, also known as the alkali metals. This is because they have only one electron in their outermost shell, making it easy to remove that electron and form a cation with a positive charge. As we move down the group, the tendency to lose an electron increases due to the decrease in ionization energy. In contrast, the elements in other groups, such as Group VIIA or the halogens, tend to gain electrons to achieve a stable octet configuration, rather than losing them.

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The statement that is not correct about the oxidation number convention is "atom of a diatomic molecule is +2". The oxidation number of an atom in a diatomic molecule depends on the molecule, and can be either positive, negative or zero. For example, in the diatomic molecule HCl, the oxidation number of H is +1 and the oxidation number of Cl is -1. In the diatomic molecule O2, the oxidation number of each O atom is 0. Therefore, the correct answer is "atom of a diatomic molecule is +2"

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An exothermic reaction is a chemical reaction that releases energy to the surrounding in the form of heat, light, or sound. This means that in an exothermic reaction, the products have lower energy than the reactants. The energy released during the reaction is given off to the surroundings, which can cause an increase in temperature or a physical change such as a phase change. Therefore, the correct option is "loss of heat to the surrounding".

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Bromine is a halogen, which means it has a high electronegativity and is very reactive towards compounds with lower electronegativities. In this case, we are looking for the compound that is most likely to react with bromine. Methane, benzene, ethyne, and hexane are all hydrocarbons, which means they are composed of hydrogen and carbon atoms. However, they differ in their chemical structures and properties. Out of these options, ethyne (also known as acetylene) is the most reactive towards bromine. This is because it has a triple bond between its two carbon atoms, which makes it more susceptible to reactions with other compounds. The triple bond is composed of two pi bonds and one sigma bond, and the pi bonds are more easily broken, allowing ethyne to react with bromine more readily. In contrast, methane and hexane have only single bonds between their carbon atoms, which makes them less reactive towards bromine. Benzene has a delocalized ring of electrons, which makes it more stable and less likely to react with other compounds, including bromine.

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The formula of the given compound is M(HCO₃)₂. The total mass of the compound is 162g per mole. We need to find the relative atomic mass of M. Let the relative atomic mass of M be x. The molecular weight of the compound will then be: Molecular weight = mass of 1 mole of the compound Molecular weight = 162g/mol The molecular weight can also be calculated as the sum of the atomic weights of all the atoms in the compound. The compound has 2 H atoms, 2 C atoms, and 6 O atoms. Using the atomic weights of H, C, and O as given in the question, we get: Molecular weight = 2x + 2(12) + 6(16) Molecular weight = 2x + 120 + 96 Molecular weight = 2x + 216 We can now equate the two expressions for the molecular weight to get: 2x + 216 = 162 2x = 162 - 216 2x = -54 x = -27 This is a non-sensical value for the relative atomic mass. The reason for this is that we made an error in the calculation. The actual molecular weight of the compound should be: Molecular weight = 2x + 2(1) + 2(12) + 6(16) Molecular weight = 2x + 122 Equating the two expressions for the molecular weight gives: 2x + 122 = 162 2x = 162 - 122 2x = 40 x = 20 Therefore, the relative atomic mass of M is 20. Answer: 40

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The reaction at the cathode during electrolysis of dilute copper (II) chloride solution can be determined by analyzing the oxidation states of the species involved. In the electrolysis of copper (II) chloride solution, the positive copper ions (Cu²⁺) migrate towards the cathode (negatively charged electrode), where they gain electrons and are reduced to form copper atoms (Cu). Therefore, the equation representing the reaction at the cathode is: Cu²⁺ + 2e^- → Cu Option (ii) represents this equation and is the correct answer.

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Limestone is needed to produce slag during the extraction of iron in the blast furnace. The blast furnace is used for extracting iron from its ore, which is a mixture mainly of iron oxide and limestone. When limestone is heated, it decomposes to form calcium oxide (CaO), which then reacts with the impurities in the ore, such as silicon dioxide (SiO2), to form slag. The slag is a waste product that floats on top of the molten iron and is removed from the furnace separately. Therefore, the correct option is B - Limestone.

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A catalyst is a substance that lowers the activation energy of a chemical reaction, which means it makes it easier for the reactants to reach the transition state and form products. This is achieved by providing an alternative reaction pathway that has a lower activation energy. Catalysts are not consumed during the reaction and can be used repeatedly. The other options, freezing mixture, reducing agent, and water, do not lower the activation energy of a chemical reaction.

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When an element with high electron affinity combines with another element with low ionization energy, the bond formed will be mainly ionic. This is because the element with high electron affinity has a strong tendency to gain electrons, while the element with low ionization energy has a low energy requirement to lose electrons. When these two elements combine, the element with high electron affinity will take one or more electrons from the element with low ionization energy to achieve a stable electron configuration. This results in the formation of positively and negatively charged ions, which are held together by electrostatic attraction to form an ionic bond. In contrast, covalent bonds involve the sharing of electrons between atoms, dative bonds involve one atom donating both electrons in the bond, and metallic bonds involve a sharing of electrons between many atoms in a metallic lattice. However, none of these types of bonds are likely to be formed when an element with high electron affinity combines with another element with low ionization energy.

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The greenhouse effect is a climatic condition associated with the presence of excess carbon (IV) oxide. When certain gases such as carbon dioxide, methane, and water vapor accumulate in the Earth's atmosphere, they trap heat from the sun and prevent it from escaping into space. This trapped heat then warms the planet's surface and leads to the greenhouse effect, which can cause significant changes to the Earth's climate and weather patterns. Carbon dioxide is the most important of these greenhouse gases, and its increasing concentration in the atmosphere due to human activities such as burning fossil fuels is a major contributor to global warming and climate change.

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A secondary alkanol is an alcohol in which the carbon atom bearing the hydroxyl group is bonded to two other carbon atoms. The correct answer is CH₃-CH(OH)-CH ₃ because the carbon bearing the hydroxyl group (-OH) is bonded to two other carbon atoms.

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An acid salt is a salt that contains an acidic ion or proton that can undergo partial hydrolysis in an aqueous solution to form an acidic solution. Among the options given, NaHCO₃ is an acid salt because it contains the acidic hydrogen carbonate ion (HCO₃^-) which can react with water to produce a slightly acidic solution. The other options, NH₄CI, MgSO₄ 7H₂O, and CH₃COONa, do not contain any acidic ion and therefore are not acid salts.

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Gas molecules are said to be perfectly elastic because they collide without loss of energy. When gas molecules collide with each other, they exchange energy and momentum, but the total energy and momentum of the molecules remain constant. This is due to the fact that gas molecules are very small and have negligible attractive forces between them. As a result, they are able to move about freely in straight lines and collide with each other in a perfectly elastic manner, without any loss of energy. Therefore, when gas molecules collide, they bounce off each other with the same energy that they had before the collision. This property of gas molecules is known as perfect elasticity, which is a key characteristic of gases.

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The energy of an electron in an atom is determined by its orbital. The orbitals with the lowest energy are filled first before the higher energy orbitals. The order of filling of orbitals is governed by Aufbau principle, which states that electrons fill the lowest energy orbital available before occupying higher energy orbitals. Based on this principle, the 4s orbital has the lowest energy among the given options, followed by 4p, 4d, and 4f in increasing order of energy. Therefore, the 4s orbital has the lowest energy. So, the answer is 4s.

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Equal volumes of CO₂ and CO at s.t.p have the same number of molecules. This is because at s.t.p, which stands for standard temperature and pressure (0 degrees Celsius and 1 atm pressure), gases occupy the same volume when they contain the same number of molecules. The molar volume of any gas at s.t.p is 22.4 liters, regardless of the gas's mass or density. Therefore, equal volumes of CO₂ and CO at s.t.p will contain the same number of molecules.

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Among the given options, the only compound that dissolves in water to form a solution with pH below 7 is ammonium chloride (NH4Cl). When NH4Cl is dissolved in water, it dissociates into ammonium ions (NH4+) and chloride ions (Cl-). The ammonium ion, NH4+, is the conjugate acid of a weak base (NH3), and it reacts with water to form hydronium ions (H3O+). This reaction produces an acidic solution with a pH below 7. On the other hand, sodium tetraoxosulphate (VI) (Na2SO4), potassium hydroxide (KOH), and sodium trioxocarbonate (IV) (Na2CO3) are all basic compounds. When they are dissolved in water, they dissociate to form hydroxide ions (OH-) which react with water to form hydroxide ions (OH-) and hydronium ions (H3O+). This reaction produces an alkaline solution with a pH greater than 7.

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Alkanoates are produced from alkanols by esterification. Esterification is a chemical reaction between an alcohol and a carboxylic acid, resulting in the formation of an ester and water. In this case, an alkanol (an alcohol with a carbon chain) reacts with a carboxylic acid to form an alkanoate (an ester with a carbon chain) and water. This process involves the removal of a hydroxyl (-OH) group from the alcohol and a hydrogen atom from the carboxylic acid, which then combine to form water. The remaining portions of the alcohol and carboxylic acid combine to form the ester (alkanoate).

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Environmental pollution problems are generally more severe in countries which have a dense population. This is because a dense population means there are more people living in a smaller area, leading to higher levels of waste generation, energy consumption, and transportation needs. As a result, the pollution levels tend to be higher due to increased industrialization and use of resources. In addition, the higher population density also leads to increased competition for resources such as land, water, and food, which can also contribute to environmental degradation.

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Gas molecules colliding in a flask can be described as random motion. When gas molecules are in motion, they collide with each other and the walls of the container in which they are enclosed. The motion of these gas molecules is completely random, and they move in different directions at different speeds. The kinetic energy of the gas molecules determines the speed and motion of the molecules. Therefore, the random motion of gas molecules is a consequence of their kinetic energy. On the other hand, the wheelbarrow being pushed, car travelling on a straight line, and planets going around the sun follow specific trajectories and patterns. They move in a specific direction and are influenced by forces acting upon them. Thus, these movements are not considered random motion.

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The reaction that is not feasible is the second one: Cl₂ + 2NaF → 2NaCI + F₂. This is because fluorine (F₂) is a more reactive halogen than chlorine (Cl₂), and as such it cannot be displaced from a compound like NaF by chlorine. This is an example of the reactivity series of halogens, where the more reactive halogens displace the less reactive halogens from their compounds.

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The Pauli Exclusion Principle is related to the quantum numbers of electrons. It states that no two electrons in an atom can have the same set of four quantum numbers (principal quantum number, azimuthal quantum number, magnetic quantum number, and spin quantum number). This principle is important in determining the electron configuration of atoms and the properties of chemical bonds between atoms. In simple terms, it means that electrons have to occupy different energy levels and different positions within those energy levels in order to form stable atoms and molecules.

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The property that increases down a group in the Periodic Table is atomic radius. Atomic radius is the distance between the nucleus of an atom and its valence electrons, which determines the size of the atom. As one goes down a group in the periodic table, the number of energy levels (shells) in the atom increases, making the atomic radius larger. This is due to the increasing distance between the nucleus and valence electrons as the number of shells increases. Therefore, the correct option is atomic radius.

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Out of the given options, the compound that is unsaturated is Methylbenzene. This is because the term "unsaturated" refers to a compound that contains at least one carbon-carbon double or triple bond. Methylbenzene, also known as toluene, has a double bond between one of its carbon atoms and the adjacent carbon atom in the benzene ring. Therefore, it is an unsaturated compound. The other options, 2-methylbutane, chloromethane, and 1,2-dibromoethane, are all saturated compounds as they contain only single bonds between their carbon atoms.

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(a)(i) Postulates of the kinetic theory of gases

1. A gas consists of a very large number of tiny particles which are in continuous rapid random motion.
2. The actual volume of the gas particles is negligible compared with the volume of the container, and intermolecular forces are negligible.
3. Collisions between gas particles and with the walls of the container are perfectly elastic. The average kinetic energy of the particles is proportional to the absolute temperature.

(a)(ii) Boyle's law

At constant temperature, the pressure of a fixed mass of gas is inversely proportional to its volume: \(P \propto \frac{1}{V}\), or \(PV=\text{constant}\).

(a)(iii) Absolute zero

Absolute zero is the lowest theoretically attainable temperature, \(0\text{ K}\) or approximately \(-273^\circ\text{C}\), at which the volume of an ideal gas would theoretically become zero and molecular motion is at its minimum.

(b)(i)

Gas X contains the greater number of molecules. For equal volumes at the same pressure,

\[n=\frac{PV}{RT}\]

Hence, \(n\propto \frac{1}{T}\). Since X is at \(200\text{ K}\), whereas oxygen is at \(800\text{ K}\), X has more molecules.

(b)(ii)

Mass of one molecule of X \(=2.19\times10^{-22}\text{ g}\).

\[M=2.19\times10^{-22}\times6.02\times10^{23}\]

\[M=(2.19\times6.02)\times10=131.8\text{ g mol}^{-1}\]

Therefore, the molar mass of X is approximately \(132\text{ g mol}^{-1}\).

(b)(iii)

\[M(\mathrm{O_2})=2(16)=32\text{ g mol}^{-1}\]

By Graham's law, rate of diffusion is inversely proportional to the square root of molar mass. Since \(32<132\), oxygen diffuses faster than X.

(c)(i) Conditions for increasing the equilibrium yield of ammonia

1. Use a high pressure, because the forward reaction changes four moles of gaseous reactants into two moles of gaseous product.
2. Use a low temperature, because the forward reaction is exothermic, \(\Delta H=-46\text{ kJ mol}^{-1}\).

Continuous removal of ammonia as it is formed also increases its yield.

(c)(ii) Labelled energy profile diagram for an endothermic reaction

(c)(iii)

Two factors, apart from temperature, which affect the rate of decomposition of W are:

1. Surface area (particle size) of W. A finely divided solid decomposes faster.
2. Presence of a catalyst.

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(a)(i) Two elements that react with steam at red heat to give hydrogen: iron (Fe) and zinc (Zn). (Magnesium is also acceptable.)

(a)(ii) Why aqueous potassium bromide turns reddish-brown with chlorine

Chlorine is a stronger oxidising agent (higher in the halogen reactivity/electrochemical series) than bromine, so it displaces bromine from the bromide solution. The reddish-brown colour is the free bromine liberated.

(a)(iii) Equation

(b)(i) Two industries that use limestone as raw material: the cement industry and the glass industry (iron and steel manufacture is also acceptable).

(b)(ii) One example of a hygroscopic substance: concentrated tetraoxosulphate(VI) acid (concentrated H\(_2\)SO\(_4\)). (Quicklime, CaO, is also acceptable.)

(b)(iii) Completed table

(c) Contact process

• (i) Sulphur(IV) oxide is obtained by burning sulphur in air/oxygen, S + O\(_2\) \(\rightarrow\) SO\(_2\), or by roasting a sulphide ore such as iron pyrites.
• (ii) In the catalyst chamber (vanadium(V) oxide catalyst, about 450 \(^{o}\)C): \[ 2\text{SO}_2 + \text{O}_2 \rightleftharpoons 2\text{SO}_3 \]
• (iii) The sulphur(VI) oxide is absorbed in concentrated tetraoxosulphate(VI) acid to form oleum, SO\(_3\) + H\(_2\)SO\(_4\) \(\rightarrow\) H\(_2\)S\(_2\)O\(_7\); the oleum is then diluted with the correct amount of water, H\(_2\)S\(_2\)O\(_7\) + H\(_2\)O \(\rightarrow\) 2H\(_2\)SO\(_4\). (SO\(_3\) is not passed directly into water because the reaction is too violent and forms an acid mist.)

(d)(i) Two disadvantages of hard water:

• It wastes soap, forming an insoluble scum before a lather is produced.
• It deposits scale (fur) in kettles, boilers and pipes, which wastes fuel and can block the pipes.

(d)(ii) Three methods that remove both permanent and temporary hardness at once: addition of washing soda (sodium trioxocarbonate(IV)), distillation, and the ion-exchange (permutit) method.

(d)(iii) Roles in town water purification:

• Alum: a coagulant - it makes fine suspended and colloidal particles clump together and settle out.
• Chlorine: a disinfectant/steriliser - it kills bacteria and other harmful micro-organisms.

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(a)

Taking R as an alkane, S as an alkene and T as a terminal alkyne:

1. Addition reaction: S and T.
2. Combustion: R, S and T.
3. Substitution reaction: R and T.

(b)

1. The process is dehydration of the alkanol.
2. The third member is propan-1-ol.
   Structural formula: CH₃CH₂CH₂OH.
3. A primary alkanol is oxidised to the corresponding alkanoic acid by excess acidified potassium manganate(VII) solution.
   For example:
   \[\mathrm{CH_3CH_2OH + 2[O] \rightarrow CH_3COOH + H_2O}\]

(c)

1. Add aqueous sodium hydrogencarbonate or sodium carbonate to the acid. Brisk effervescence of carbon dioxide is produced.
   \[\mathrm{RCOOH + NaHCO_3 \rightarrow RCOONa + CO_2 + H_2O}\]
2. \[\mathrm{HCOOH + CH_3CH_2OH \xrightleftharpoons[\ ]{conc.\ H_2SO_4} HCOOCH_2CH_3 + H_2O}\]

   The ester formed is ethyl methanoate.

3. The mineral acid acts as a catalyst in the esterification reaction.

(d)

1. H is carbon dioxide, CO₂.
2. Starch is a polysaccharide. The diastase (amylase) enzyme in malt hydrolyses starch to maltose, a reducing sugar.
   \[\mathrm{(C_6H_{10}O_5)_n + \tfrac{n}{2}H_2O \xrightarrow[55^{\circ}C]{diastase} \tfrac{n}{2}C_{12}H_{22}O_{11}}}\]

   Yeast subsequently ferments the sugar to ethanol, J, and carbon dioxide:

   \[\mathrm{C_6H_{12}O_6 \xrightarrow{yeast} 2C_2H_5OH + 2CO_2}\]
3. J is ethanol. A sample is obtained from the fermented mixture by simple distillation.

Distillation set-up for obtaining ethanol (J)

The fermented mixture is heated gently in a water bath. Ethanol distils over, condenses in the Liebig condenser and is collected as the distillate.

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(a)(i) Differences between a conductor and an electrolyte

(a)(ii) Three applications of electrolysis

• Electroplating of metals.
• Purification (refining) of metals such as copper.
• Extraction of reactive metals (e.g. sodium, aluminium) and manufacture of chemicals (NaOH, Cl₂).

(a)(iii) Electrode reactions for dilute NaCl (carbon electrodes)

Cathode (reduction): \( 2\text{H}^+_{(aq)} + 2e^- \to \text{H}_{2(g)} \)

Anode (oxidation): \( 4\text{OH}^-_{(aq)} \to \text{O}_{2(g)} + 2\text{H}_2\text{O}_{(l)} + 4e^- \)

(Because the solution is dilute, oxygen, not chlorine, is discharged at the anode.)

(b)(i) An electrochemical cell is a device in which a redox reaction is used to convert chemical energy into electrical energy (or, in electrolysis, electrical energy into chemical energy).

(b)(ii) Primary cells: the Daniell cell and the dry Leclanche (zinc-carbon) cell.

(b)(iii) Half-cell equations for Mg + Fe²⁺ \(\to\) Mg²⁺ + Fe

Oxidation: \( \text{Mg} \to \text{Mg}^{2+} + 2e^- \)

Reduction: \( \text{Fe}^{2+} + 2e^- \to \text{Fe} \)

(c)(i) Quantity of electricity

\( t = 3\,\text{h}\,20\,\text{min} = 12000\ \text{s} \)

\[ Q = It = 0.72 \times 12000 = 8640\ \text{C} \]

(c)(ii) At the cathode H₂ is evolved, at the anode O₂; by the equation \(2\text{H}_2\text{O} \to 2\text{H}_2 + \text{O}_2\) the volume ratio H₂:O₂ is 2:1. So for 1 dm³ of H₂ at the cathode, the anode gives 0.5 dm³ of O₂.

(d)(i) Mass of CuO in excess

CuO + H₂SO₄ \(\to\) CuSO₄ + H₂O (1 : 1)

\[ n(\text{CuO}) = \frac{20}{64+16} = \frac{20}{80} = 0.25\ \text{mol} \]

Only 0.05 mol reacts (limited by acid), so excess CuO = \(0.25 - 0.05 = 0.20\) mol.

\[ \text{mass in excess} = 0.20 \times 80 = 16\ \text{g} \]

(d)(ii) A neutralization (acid-base) reaction.

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(a)(i) Differences between covalent and electrovalent compounds

(a)(ii) Electronic structures and groups

• K (atomic number 12): 2, 8, 2 — Group II.
• L (atomic number 8): 2, 6 — Group VI.

(a)(iii) No. An alkali metal is very electropositive and reactive; it holds oxygen far more strongly than carbon does, so its oxide cannot be reduced by coke (carbon). Such metals are extracted by electrolysis of their molten salts.

(b)(i) Half-life: the time taken for half of the atoms (nuclei) in a given sample of a radioactive element to decay.

(b)(ii) Carbon-14 (\(^{14}_{6}\text{C}\)).

(b)(iii) Balancing mass and charge numbers, aluminium-28 decays by beta emission to silicon-28:

\[ ^{28}_{13}\text{Al} \to\ ^{28}_{14}\text{Si} + ^{\ \ 0}_{-1}\text{Q} \]

Q is a beta particle (electron), \(^{\ \ 0}_{-1}e\).

(c)(i) Three chemical properties of metals

• React with oxygen to form basic oxides.
• React with dilute acids to liberate hydrogen gas.
• Displace less reactive metals from their salt solutions (they act as reducing agents, losing electrons).

(c)(ii) Duralumin is light (low density) yet strong, and it is resistant to corrosion.

(c)(iii) Malleability.

(c)(iv) Moles of electrons

\[ n(\text{Fe}) = \frac{2.8}{56} = 0.05\ \text{mol} \]

Fe \(\to\) Fe²⁺ + 2e^-, so:

\[ n(e^-) = 2 \times 0.05 = 0.10\ \text{mol} \]