Mix Examples of General Principles and processes of Isolation of Elements Questions in English

(D) The correct matches are as follows:
$A$. Sulphuric acid is manufactured by the $iv$. Contact process.
$B$. Steel is manufactured by the $ii$. Bessemer's process.
$C$. Sodium hydroxide was historically manufactured by the $iii$. Leblanc process.
$D$. Ammonia is manufactured by the $i$. Haber's process.
Therefore,the correct matching is $A-iv, B-ii, C-iii, D-i$.

(B) The extraction of metals from their ores involves several steps such as concentration,roasting/calcination,reduction,and refining.
$A$. $ZnCO_3 \rightarrow Zn$ involves calcination followed by reduction ($2$ steps).
$B$. $CuFeS_2 \rightarrow Cu$ involves concentration,roasting,smelting,bessemerization,and electrolytic refining (more than $2$ steps).
$C$. $PbS \rightarrow Pb$ involves roasting followed by reduction ($2$ steps).
Since $CuFeS_2$ extraction involves multiple complex steps including concentration,roasting,smelting,and refining,it clearly involves more than two metallurgical processes.

(A) In the metallurgy of iron,limestone $(CaCO_3)$ is added to the blast furnace as a flux.
Inside the furnace,$CaCO_3$ decomposes to form lime $(CaO)$ and carbon dioxide $(CO_2)$:
$CaCO_3 \rightarrow CaO + CO_2$
The lime $(CaO)$ then reacts with silica $(SiO_2)$,which is an acidic impurity (gangue) present in the ore,to form calcium silicate $(CaSiO_3)$:
$CaO + SiO_2 \rightarrow CaSiO_3$
This calcium silicate $(CaSiO_3)$ is known as slag,which is molten and floats on top of the molten iron.
Therefore,the calcium ions end up in the slag.

(D) For the extraction of lead from low-grade ore,the following steps are involved:
$1$. Froth floatation $(a)$: Used to concentrate the ore by removing gangue particles.
$2$. Roasting $(c)$: The concentrated ore is heated in the presence of air to convert lead sulfide $(PbS)$ into lead oxide $(PbO)$.
$3$. Smelting $(f)$: The roasted ore is reduced using coke $(C)$ in a blast furnace to obtain metallic lead $(Pb)$.
Therefore,the correct sequence is $a$ $\rightarrow c$ $\rightarrow f$.

(A) True: In the cupellation process,lead is oxidized to $PbO$ and removed,leaving behind pure silver.
$(b)$ True: Froth flotation can be used for non-sulphide ores (like oxides or carbonates) by using specific activators or collectors.
$(c)$ False: The electrolyte used for the electrolytic refining of $Pb$ is $PbSiF_6$ (lead fluosilicate) with $H_2SiF_6$ (hydrofluosilicic acid),not $PbSO_4$.
$(d)$ True: According to the Ellingham diagram,a metal can only reduce the oxide of a metal that lies above it (i.e.,has a more positive $\Delta G$ value at that temperature).
Therefore,the sequence is $T, T, F, T$.

(D) Pyro metallurgy involves the extraction of metals by heating ores at high temperatures,which is used for $Fe$ (iron) in a blast furnace.
Hydro metallurgy involves the extraction of metals using aqueous solutions,which is used for $Au$ (gold) via cyanide leaching.
Since both statements are correct,the correct option is $D$.

(D) The extraction of zinc from zinc blende $(ZnS)$ involves the following steps:
$1$. Concentration of the ore by the $Froth \ flotation \ method$.
$2$. $Roasting$ of the concentrated ore to convert $ZnS$ into $ZnO$.
$3$. $Smelting$ (reduction) of $ZnO$ with coke to obtain zinc metal.
$4$. The zinc obtained is purified by $Distillation$.
However,the question asks for a process not used for the extraction of $spelter$ (impure zinc). All the listed processes are standard steps in the extraction of zinc. If we consider the context of the extraction process,$Froth \ flotation$,$Roasting$,$Smelting$,and $Distillation$ are all integral parts of the industrial production of zinc. Given the options,if the question implies a step not directly involved in the chemical reduction or purification,it is often a trick question. However,technically,all are used. If forced to choose,$Froth \ flotation$ is a concentration method,not an extraction method. Thus,it is the most distinct.

(D) Ellingham diagrams are graphical representations of the variation of the standard Gibbs free energy of formation $({\Delta}G^{\circ})$ of compounds with temperature.
They are primarily used to predict the feasibility of the reduction of metal oxides,sulphides,and halides using a suitable reducing agent.
Therefore,Ellingham diagrams can be constructed for all these classes of compounds.

(B) According to the Ellingham diagram principle,a metal oxide can be reduced by a reducing agent if the line of the reducing agent lies below the line of the metal oxide at that temperature.
$1$. Since the oxide of $M$ cannot be reduced by carbon up to $800\, ^\circ C$,the line for $M$ must lie below the lines for $C \rightarrow CO_2$ and $C \rightarrow CO$ up to $800\, ^\circ C$.
$2$. Since the oxide of $M$ can be reduced by $Al$ below $800\, ^\circ C$,the line for $Al$ must lie below the line for $M$ at temperatures below $800\, ^\circ C$.
$3$. Combining these,the line for $M$ must be above the line for $Al$ but below the lines for carbon oxidation at temperatures below $800\, ^\circ C$. This corresponds to the diagram in option $B$.

(A) The Bessemer process is a metallurgical process used for the extraction and purification of metals.
It involves blowing air through molten metal to oxidize impurities.
This process is primarily used for the conversion of pig iron into steel $(Fe)$ and for the extraction of copper $(Cu)$ from copper matte in a Bessemer converter.
Therefore,Bessemerisation is carried out for $Fe$ and $Cu$.

(D) Statement $(a)$ is incorrect because calcination and roasting are typically performed in a reverberatory furnace,not a blast furnace.
Statement $(b)$ is correct; the impurities like sand,clay,or rocks present in the ore are known as gangue or matrix.
Statement $(c)$ is correct; the froth floatation process is specifically used for the concentration of sulphide ores based on the preferential wetting of the ore particles by oil.
Therefore,both $(b)$ and $(c)$ are correct statements.

(C) In the extraction of iron from haematite $(Fe_2O_3)$,$SiO_2$ is an impurity (gangue) that must be removed by adding a flux like $CaO$ to form $CaSiO_3$ slag. Therefore,$SiO_2$ is undesirable in iron extraction.
In the extraction of copper from copper pyrites $(CuFeS_2)$,$FeO$ is formed as an impurity during roasting. $SiO_2$ is added as a flux to react with $FeO$ to form $FeSiO_3$ (slag),which is easily removed. Thus,$SiO_2$ is a desirable substance in copper extraction.

(C) van Arkel method is used for the purification of metals like titanium $(Ti)$ and zirconium $(Zr)$. So,$(a-2)$.
$(b)$ Solvay process is used for the manufacture of sodium carbonate $(Na_2CO_3)$. So,$(b-3)$.
$(c)$ Cupellation is a refining process used for the purification of silver $(Ag)$ from lead $(Pb)$. So,$(c-5)$.
$(d)$ Poling is a process used for the removal of cuprous oxide $(Cu_2O)$ from blister copper. So,$(d-4)$.
Therefore,the correct matching is $(a-2, b-3, c-5, d-4)$.

(D) The process described is known as $quenching$. When steel is heated to a high temperature (red heat) and then rapidly cooled by plunging it into cold water or oil,the internal structure of the steel changes. This rapid cooling prevents the formation of softer phases and results in the formation of martensite,which is a very hard and brittle phase of steel. Therefore,this treatment makes the steel hard and brittle.

(C) $(i)$ $Cu_2S$ is reduced by $Cu_2O$ (self-reduction),not by $FeS$. $FeS$ is used to remove $FeO$ as slag. So,statement $(i)$ is $F$.
$(ii)$ $FeCrO_4$ (chromite) is magnetic,and $SnO_2$ (cassiterite) is non-magnetic. Thus,magnetic separation is used. So,statement $(ii)$ is $T$.
$(iii)$ $Cu$ is extracted by self-reduction of $Cu_2S$ with $Cu_2O$,and $Hg$ is extracted by roasting $HgS$ to $HgO$ followed by self-reduction. So,statement $(iii)$ is $T$.
$(iv)$ Cassiterite is $SnO_2$ and Rutile is $TiO_2$. Both are oxide ores. So,statement $(iv)$ is $T$.
The correct order is $FTTT$.

(D) Statement $A$ is correct: Liquation is used for metals with low melting points (e.g.,$Sn, Pb, Bi$) compared to impurities.
Statement $B$ is correct: $Fe_3C$ (cementite) formation increases the hardness of steel.
Statement $C$ is correct: Metals like $Hg$ $(HgS + O_2 \rightarrow Hg + SO_2)$ and $Cu$ ($2Cu_2S + 3O_2 \rightarrow 2Cu_2O + 2SO_2$; $2Cu_2O + Cu_2S \rightarrow 6Cu + SO_2$) are extracted via auto-reduction.
Statement $D$ is incorrect: The amalgamation process is specifically used for the extraction and purification of noble metals like $Au$ and $Ag$ because they form amalgams with mercury.

(B) $I$. Explosive: $Pb(NO_3)_2$ is known to be explosive upon heating.
$II$. Self-reduction: $Cu$ is obtained from its sulfide ores by self-reduction process ($2Cu_2S + 3O_2 \rightarrow 2Cu_2O + 2SO_2$; $2Cu_2O + Cu_2S \rightarrow 6Cu + SO_2$).
$III$. Magnetic material: $Fe_3O_4$ (Magnetite) is a well-known magnetic material.
$IV$. Verdigris: $Cu(CH_3COO)_2 \cdot Cu(OH)_2$ is the chemical formula for verdigris,a green pigment formed on copper surfaces.
Therefore,the correct match is $I-D, II-A, III-B, IV-C$.

(A) $1)$ The percentage of silver in German silver is $0 \%$.
$2)$ German silver is an alloy consisting of copper,zinc,and nickel. Its typical composition is approximately $50 \%$ to $61.6 \%$ copper,$19 \%$ to $17.2 \%$ zinc,and $30 \%$ to $21.1 \%$ nickel.
$3)$ Despite its name,it contains no silver. Therefore,option $A$ is correct.

(B) The extraction of iron from haematite $(Fe_2O_3)$ involves the reduction of iron oxide to metallic iron using carbon monoxide $(CO)$ or coke $(C)$ in a blast furnace. This is a reduction process.
Subsequently,the conversion of pig iron into steel involves the removal of impurities like carbon,silicon,manganese,phosphorus,and sulfur by oxidation.
Therefore,the overall process involves reduction (to obtain iron) followed by oxidation (to refine it into steel).

(D) Railway wagon axles are made by heating rods of iron embedded in charcoal powder. This process is known as case hardening.
The process of hardening the surface of wrought iron by depositing a surface layer of steel on it is called case hardening. It is done by heating wrought iron in contact with carbonaceous materials like charcoal. This increases the carbon content on the surface,making it harder and more durable.

(B) $I.$ Cyanide process is used for the extraction of $Au$ (Gold) and $Ag$ (Silver).
$II.$ Froth Floatation process is used for the concentration of sulphide ores like $HgS$ (Cinnabar).
$III.$ Electrolytic reduction is used for the extraction of highly reactive metals like $Al$ (Aluminium).
$IV.$ Zone refining is used for the purification of semiconductors like $Ge$ (Germanium) and $Si$ (Silicon).
Therefore,the correct matching is $I-(4), II-(2), III-(3), IV-(1)$.

(D) The given chemical equation represents the MacArthur-Forrest process,which is used for the extraction of noble metals like gold $(Au)$ and silver $(Ag)$ from their ores.
The balanced equation for the dissolution of these metals in cyanide solution is:
$4M + 8CN^{-} + 2H_2O + O_2 \rightarrow 4[M(CN)_2]^- + 4OH^{-}$
Here,$M$ represents either $Au$ or $Ag$.
Therefore,both $(a)$ and $(b)$ are correct.

(C) In extractive metallurgy,a reaction is entropy-driven if the change in entropy $(\Delta S)$ is positive,which usually occurs when the number of moles of gaseous products is greater than the number of moles of gaseous reactants.
$A$: $CaCO_{3} \cdot MgCO_{3(s)} \to CaO_{(s)} + MgO_{(s)} + 2CO_{2(g)}$. Here,$\Delta n_g = 2 - 0 = 2 > 0$. Entropy increases.
$B$: $C_{(s)} + CO_{2(g)} \to 2CO_{(g)}$. Here,$\Delta n_g = 2 - 1 = 1 > 0$. Entropy increases.
$C$: $2Cu_{2}S + 3O_{2(g)} \to 2Cu_{2}O + 2SO_{2(g)}$. Here,$\Delta n_g = 2 - 3 = -1 < 0$. Entropy decreases.
$D$: $Ni(CO)_{4(g)} \to Ni_{(s)} + 4CO_{(g)}$. Here,$\Delta n_g = 4 - 1 = 3 > 0$. Entropy increases.
Since reaction $C$ results in a decrease in the number of gaseous moles,it is not entropy-driven.

(A) Monel metal is an alloy primarily composed of nickel ($Ni$,$65-70\%$) and copper ($Cu$,$20-29\%$),with small amounts of iron and manganese.
Gun metal is an alloy of copper,tin,and zinc.
Solder is an alloy of lead and tin.
$14$ carat gold is an alloy of gold,silver,and copper.
Therefore,the correct option is $A$.

(B) $1$. Cerrusite is $PbCO_3$ (a carbonate ore),which is concentrated by gravity separation or froth floatation,but it is not the primary method. However,statement $A$ is generally considered acceptable in some contexts.
$2$. In the extraction of iron,the process involves calcination and smelting in a blast furnace,not roasting. Roasting is typically used for sulfide ores. Thus,statement $B$ is incorrect.
$3$. Serpeck's process is used for the purification of bauxite $(Al_2O_3)$. The byproduct is $AlN$ (Aluminum Nitride),not silicon. Thus,statement $C$ is also incorrect.
$4$. Cassiterite $(SnO_2)$ and Rutile $(TiO_2)$ are indeed oxide ores.
Given the standard curriculum,both $B$ and $C$ contain inaccuracies,but $B$ is a fundamental error regarding iron metallurgy.

(D) $1$. Froth floatation is based on the principle of differential wettability of ore and gangue particles by oil and water. This is correct.
$2$. $NaCN$ is used as a depressant to selectively prevent $ZnS$ from forming froth in the presence of $PbS$. This is correct.
$3$. Calamine is $ZnCO_3$,which is a carbonate ore. This is correct.
$4$. Malachite is a copper ore with the formula $CuCO_3 \cdot Cu(OH)_2$. Therefore,the statement that it is an ore of $Zn$ is incorrect.

(A) . Silver $(Ag)$ is a noble metal and occurs in the native (free) state in nature.
$B$. Chromium oxide $(Cr_2O_3)$ is reduced to chromium metal using aluminum powder in the Aluminothermic process.
$C$. The van Arkel method is specifically used for the purification of metals like Titanium $(Ti)$ and Zirconium $(Zr)$ by forming volatile iodides.
$D$. Auto-reduction (or self-reduction) is used for sulphide ores of less electropositive metals like Mercury $(Hg)$,Lead $(Pb)$,and Copper $(Cu)$.
Therefore,the correct matching is: $A-S, B-R, C-Q, D-P$.

(B) The correct answer is $B$.
$A$. Tin $(Sn)$ is extracted from its ore cassiterite $(SnO_2)$ by reduction with carbon (smelting). This is correct.
$B$. Aluminium $(Al)$ is extracted by the Hall-$H$éroult process,which involves the electrolytic reduction of alumina $(Al_2O_3)$ dissolved in molten cryolite $(Na_3AlF_6)$. It does not involve carbon reduction of the oxide. Therefore,this statement is incorrect.
$C$. Bessemerisation is a process primarily used for the extraction of copper from copper matte. It is not involved in the extraction of lead. This is correct.
$D$. Silver $(Ag)$ is extracted by the Mac-Arthur Forrest cyanide process,where the ore is treated with a dilute solution of $NaCN$ or $KCN$. This is correct.

(D) $1$. Tin stone $(SnO_2)$ is non-magnetic,while wolframite $(FeWO_4 + MnWO_4)$ is magnetic. Electromagnetic separation is used to remove magnetic impurities from non-magnetic ores. Thus,statement $A$ is correct.
$2$. In the blast furnace,$CO$ is the primary reducing agent in the upper and middle zones,while $C$ acts as a reducing agent in the lower zone. Thus,statement $B$ is correct.
$3$. During the extraction of $Cu$ from $CuFeS_2$,$FeO$ reacts with $SiO_2$ to form $FeSiO_3$ (slag). During the extraction of iron from haematite,$CaO$ (from limestone) reacts with $SiO_2$ to form $CaSiO_3$ (slag). Thus,statement $C$ is correct.
$4$. Since all statements $A, B,$ and $C$ are correct,the correct choice is $D$.

(C) $1$. In an Ellingham diagram,the metal whose line lies lower can reduce the oxide of the metal whose line lies higher. Thus,if $M$ is below $M'O$,$M$ can reduce $M'O$ to $M'$. This statement is correct.
$2$. Oxides of alkaline earth metals (like $CaO$,$MgO$) are basic in nature. They react with acidic oxides (like $CO_2$,$SO_2$) present in the atmosphere to form carbonates or sulfites (salts). This statement is also correct.
$3$. Therefore,both statements are correct.

(D) $1$. $Pb$ (Lead) is extracted from Galena $(PbS)$ primarily by self-reduction of its oxide $(PbO)$ with the remaining sulfide $(PbS)$.
$2$. $Cu$ (Copper) is refined using the poling process,where molten copper is stirred with green wood poles to reduce copper$(I)$ oxide $(Cu_2O)$ to copper metal.
$3$. $Ag$ (Silver) is extracted via the Mac-Arthur Forrest cyanide process,which involves leaching silver ore with a dilute solution of $NaCN$ or $KCN$ in the presence of air.
$4$. Since all these processes are standard metallurgical techniques for the respective metals,the correct option is $D$.

(A) $Cu$ (Copper) is present in brass,bronze,and German silver.
Brass is an alloy of $Cu$ and $Zn$.
Bronze is an alloy of $Cu$ and $Sn$.
German silver is an alloy of $Cu$,$Zn$,and $Ni$.
Therefore,$Cu$ is the common metal present in all these alloys.

(A) $(P). [M(CN)_2]^-$ is formed during the leaching of $Ag$ ore (MacArthur-Forrest process).
$(Q). [M(CO)_4]$ is $Ni(CO)_4$,formed during the Mond process for the refining of $Ni$.
$(R). MI_4$ is $TiI_4$,formed during the van Arkel method for the refining of $Ti$.
$(S). MO$ is $PbO$,formed during the roasting of $PbS$ ore.
Therefore,the correct matching is $P-4, Q-1, R-2, S-3$.

(A) $(P) \ PbS + 2PbO \xrightarrow{\Delta} 3Pb + SO_2 \uparrow$ is an example of self-reduction.
$(Q) \ PbS + \frac{3}{2}O_2 \xrightarrow{\Delta} PbO + SO_2 \uparrow$ is roasting (heating in excess of air).
$(R) \ PbCO_3 \xrightarrow{\Delta} PbO + CO_2 \uparrow$ is calcination (heating in limited supply of air).
$(S) \ PbO + C \xrightarrow{\Delta} Pb + CO \uparrow$ is smelting (reduction using carbon).
Therefore,the correct matching is $P-2, Q-4, R-3, S-1$.

(B) In the extraction of iron,haematite $(Fe_2O_3)$ is reduced to pig iron in a blast furnace using coke and limestone. This is a correct match.
Copper matte is a mixture of $Cu_2S$ and $FeS$,and its conversion to $Cu$ involves Bessemerization (self-reduction),but the option is often considered incomplete or less accurate compared to the blast furnace process for iron.
Galena $(PbS)$ is converted to $PbO$ by roasting (not calcination).
Red bauxite is purified by the Bayer process,and $Al$ is obtained by Hall-Heroult electrolytic reduction,but the process sequence is distinct.

(D) Statement $(I)$ is correct: $Al$ is a stronger reducing agent than $Cr$ because the formation of $Al_2O_3$ is more exothermic than $Cr_2O_3$.
Statement $(II)$ is correct: $Al$ is used in the thermite process to reduce $Fe_2O_3$ to $Fe$.
Statement $(III)$ is correct: $PbO$ is reduced to $Pb$ by carbon in a blast furnace.
Statement $(IV)$ is correct: $SnO_2$ is reduced to $Sn$ by carbon (smelting).
Since all statements are correct,the correct option is $D$.

(B) Solder is an alloy composed of $Sn$ (Tin) and $Pb$ (Lead). Therefore,it contains $Sn$ metal. The composition is typically $Sn + Pb$.

(A) The correct matches are as follows:
$(P) \ [M(CN)_2]^-$: This complex is formed by $Ag$ during the leaching of ore (MacArthur-Forrest process).
$(Q) \ [M(CO)_4]$: This corresponds to $Ni(CO)_4$,which is formed during the Mond process for the refining of $Ni$.
$(R) \ MI_4$: This corresponds to $TiI_4$,which is formed during the Van Arkel method for the refining of $Ti$.
$(S) \ MO$: This corresponds to $PbO$,which is formed during the roasting of lead ore $(PbS)$.
Thus,the correct sequence is $P-4, Q-1, R-2, S-3$.

(A) The composition of the given alloys is as follows:
$1$. Gun metal $= Cu + Sn + Zn$
$2$. Solder $= Sn + Pb$
$3$. Bell metal $= Cu + Sn$
$4$. German silver $= Ni + Zn + Cu$
Therefore,the alloy containing $Cu$,$Sn$,and $Zn$ is Gun metal.

(D) The correct answer is $D$.
$Al$ is extracted by the electrolytic reduction of fused $Al_2O_3$ mixed with $Na_3AlF_6$ (cryolite) and $CaF_2$ (fluorspar) to lower the melting point and increase conductivity.
Aqueous $Al_2(SO_4)_3$ cannot be used for the electrorefining of $Al$ because $Al$ is more reactive than $H_2$ and would react with water to produce $H_2$ gas instead of depositing $Al$ at the cathode.
Option $A$ is correct as pine oil acts as a frother.
Option $B$ is correct as poling is used to remove impurities like $Cu_2O$ from molten copper.
Option $C$ is correct as dolomite is $CaCO_3 \cdot MgCO_3$.

(A) In the leaching of bauxite $(Al_2O_3 \cdot 2H_2O)$,the ore contains impurities like $SiO_2$,$Fe_2O_3$,and $TiO_2$.
When treated with concentrated $NaOH$ solution,$Al_2O_3$ dissolves to form sodium aluminate $(Na[Al(OH)_4])$ and $SiO_2$ dissolves to form sodium silicate $(Na_2SiO_3)$.
Thus,option $A$ is correct.
Option $B$ is incorrect because the Hall-Heroult process is used only for aluminium.
Option $C$ is incorrect because the blistered appearance of copper is due to the evolution of $SO_2$ gas,not $CO_2$.
Option $D$ is incorrect because cast iron is obtained from pig iron.

(C) An alloy is a mixture of two or more metals or a metal and a non-metal.
$A$. Brass is an alloy of $Cu$ and $Zn$ (both metals).
$B$. Bronze is an alloy of $Cu$ and $Sn$ (both metals).
$C$. Stainless steel is an alloy of $Fe$,$Cr$,$Ni$,and $C$ (carbon is a non-metal).
$D$. Alnico is an alloy of $Al$,$Ni$,$Co$,and $Fe$ (all metals).
Therefore,stainless steel is the correct answer as it contains carbon as a non-metal.

(A) Thomas slag is a byproduct obtained during the manufacture of steel from phosphatic iron ore by the basic Bessemer process. It consists mainly of calcium phosphate,$Ca_3(PO_4)_2$,and calcium silicate,$CaSiO_3$. Due to its composition,it is primarily used as a fertilizer and in road making and as a building material.

(D) In the extraction of copper from copper pyrites $(CuFeS_2)$,the following by-products are obtained:
$1$. Gold and silver are recovered from the anode mud during electrolytic refining.
$2$. $FeSiO_3$ (iron silicate) is formed as slag,which is used in road making.
$3$. $SO_2$ gas is released,which is captured and used for the manufacture of $H_2SO_4$ by the contact process.
$4$. $FeSO_4$ (ferrous sulfate) is $NOT$ a by-product obtained in the extraction of copper. Therefore,option $D$ is the correct answer.

(B) Statement $1$ is $F$ (False): $SnO_2$ (cassiterite) is non-magnetic,while wolframite $(FeWO_4 + MnWO_4)$ is magnetic. Electromagnetic separation is used to separate them.
Statement $2$ is $T$ (True): Argentite $(Ag_2S)$ is a sulfide ore and is concentrated by the froth floatation process.
Statement $3$ is $T$ (True): Copper and lead ores (like $Cu_2S$ and $PbS$) are extracted by self-reduction (autoreduction) after partial roasting.
Statement $4$ is $T$ (True): In the blast furnace for $Fe$ extraction,$CO$ acts as a reducing agent at lower temperatures (e.g.,$500-800 \ K$ range).
Therefore,the sequence is $F, T, T, T$.

(A) The correct matches are as follows:
$A$. Van Arkel method is used for the purification of metals like titanium and zirconium $(A-P)$.
$B$. Solvay process is used for the industrial manufacture of sodium carbonate $(Na_2CO_3)$ $(B-Q)$.
$C$. Bassemerisation is a process used in the extraction of copper to reduce copper matte $(Cu_2S + FeS)$ to blister copper $(C-S)$.
$D$. Hall-Herault process is the electrolytic reduction of alumina $(Al_2O_3)$ to obtain aluminium $(D-R)$.
Therefore,the correct sequence is $A-P, B-Q, C-S, D-R$.

(C) The $van \ Arkel$ method is used for the refining of $Zr$ and $Ti$.
$Kroll's$ process is used for the extraction of $Ti$.
$Distillation$ is used for the purification of volatile metals like $Zn$ and $Hg$.
$Froth \ Floatation$ is primarily used for sulphide ores. $Cerussite$ $(PbCO_3)$ is a carbonate ore,so it is concentrated by gravity separation or magnetic separation,not by froth floatation.
Hence,Option $C$ is the incorrectly matched pair.

(A) Bessemerisation is a metallurgical process used for the extraction of metals.
In the case of $Fe$ (iron),the Bessemer process is used to remove impurities like carbon,silicon,and manganese from molten pig iron by blowing air through it.
In the case of $Cu$ (copper),the Bessemer converter is used to convert molten matte $(Cu_2S + FeS)$ into blister copper by blowing air,which oxidizes $FeS$ to $FeO$ and then removes it as slag,followed by the self-reduction of $Cu_2S$ to $Cu$.
Therefore,Bessemerisation is carried out for $Fe$ and $Cu$.

(A) The incorrect match is $A$.
Baeyer's method is used for the concentration of bauxite ore $(Al_2O_3 \cdot 2H_2O)$,not for the purification of $Al$ metal.
Purification of $Al$ metal is typically done by Hoop's electrolytic process.