Match the items of Column I
Question: Match the items of Column I with items of Column II and assign the correct code: Code : (i) A (1) B (2) C (3) D (4) (ii) A (2) B (4) C (5) D (3) (iii) A (2) B (3) C (4) D (5) (iv) A (4) B (5) C (3) D (2) Solution: Option (ii)A (2) B (4) C (5) D (3)is the answer....
Read More →Write the chemical reactions involved
Question: Write the chemical reactions involved in the extraction of gold by the cyanide process. Also, give the role of zinc in the extraction. Solution: 4Au(s) + 8CN (aq) + 2H2O(aq) + O2(g) 4[Au(CN)2] (aq) + 4OH (aq) 2[Au(CN)2] (aq) + Zn(s) 2Au(s) + [Zn(CN)4] 2 (aq) Zinc places the role of a reducing agent. It reduces Au+ to pure Au....
Read More →Show that the function
Question: Show that the function $f: N \rightarrow Z$, defined by $\mathrm{f}(\mathrm{n})=\left\{\begin{array}{l}\frac{1}{2}(\mathrm{n}-1), \text { when } \mathrm{n} \text { is odd } \\ -\frac{1}{2} \mathrm{n}, \text { when } \mathrm{n} \text { is even }\end{array}\right.$ is both one - one and onto. Solution: $f(n)=\left\{\begin{array}{l}\frac{1}{2}(n-1), \text { when } n \text { is odd } \\ -\frac{1}{2} n, \text { when } n \text { is even }\end{array}\right.$ $f(1)=0$ $f(2)=-1$ $f(3)=1$ $f(4)=...
Read More →Give two requirements for vapour phase refining.
Question: Give two requirements for vapour phase refining. Solution: (i) The metal should react easily with the reagent to form the complex. (ii) The volatile complex should easily decomposable so that the recovery is easy....
Read More →Write down the reactions taking place in Blast
Question: Write down the reactions taking place in Blast furnace-related to the metallurgy of iron in the temperature range 500-800 K. Solution: These are the reactions that happen in the blast furnace at the 500K-800K range. 3Fe2O3 + CO 2Fe3O4 + CO2 Fe3O4 + CO 3FeO + 2CO2 Fe2O3 + CO 2FeO + CO2...
Read More →How are metals used as semiconductors refined?
Question: How are metals used as semiconductors refined? What is the principle of the method used? Solution: Semiconductors are refined by zone refining. Zone refining is based on the principle that impurities are more soluble in the molten metal than in the solid metal. A molten zone moves along the impure rod heating it, the impurities dissolve in the molten zone and move along the rod, while the pure metal devoid of impurities gets left behind and crystallises out....
Read More →What is the role of flux in metallurgical
Question: What is the role of flux in metallurgical processes? Solution: To remove gangue, certain substances are mixed with it. These are called fluxes. Flux can be basic or acidic. Acidic flux removes basic impurity and basic flux removes acidic impurity. Flux is also used for increased conductivity....
Read More →Prove that the function
Question: Prove that the function $f: N \rightarrow N: f(n)=\left(n^{2}+n+1\right)$ is one - one but not onto. Solution: In the given range of $N f(x)$ is monotonically increasing. $\therefore f(n)=n^{2}+n+1$ is one one. But Range of $f(n)=[0.75, \infty) \neq N$ (codomain) Hence, $f(n)$ is not onto. Hence, proved that the function $f: N \rightarrow N: f(n)=\left(n^{2}+n+1\right)$ is one - one but not onto....
Read More →What should be the considerations during
Question: What should be the considerations during the extraction of metals by electrochemical method? Solution: (i) Reactivity of the metal produced (ii) Electrodes to be made of suitable material (iii) Addition of flux for making molten mass conducting...
Read More →Which method is used for refining Zr
Question: Which method is used for refining Zr and Ti? Explain with the equation. Solution: Van Arkel method is used for refining Zr and Ti. Van Arkel process involves heating the impure metal with Iodine. It forms a volatile complex which on decomposition at high temperatures, gives back the metal but in very pure form. Refining of Zr and Ti using Van Arkel method For Zirconium, Zr(impure) + 2I2 ZrI4 ZrI4Zr(pure) + 2I2 (at 1800K) For Titanium, Ti(impure) + 2I2 TiI4 TiI4 Ti(pure) + 2I2 (at 1800K...
Read More →Why are sulphide ores converted
Question: Why are sulphide ores converted to oxide before reduction? Solution: Sulphide ores cannot be easily reduced so they are usually converted to oxides because oxides can be reduced easily....
Read More →Why is sulphide ore of copper heated
Question: Why is sulphide ore of copper heated in a furnace after mixing with silica? Solution: Sulphide ore of copper is heated in a furnace after mixing with silica because the iron impurities present in the ore can form slag with silica and will be easily removed. The copper is produced as copper matte. FeO + SiO2 FeSiO3(slag)...
Read More →Show that the function
Question: Show that the function $f: R \rightarrow R: f(x)=\sin x$ is neither one - one nor onto. Solution: $f(x)=\sin x$ $y=\sin x$ Here in this range, the lines cut the curve in 2 equal valued points of $y$, therefore, the function $f(x)=$ sin $x$ is not one - one. Range of $f(x)=[-1,1] \neq R$ (codomain) $\therefore f(x)$ is not onto. Hence, showed that the function $f: R \rightarrow R: f(x)=\sin x$ is neither one - one nor onto....
Read More →The mixture of compounds A and B
Question: The mixture of compounds A and B is passed through a column of Al2O3 by using alcohol as eluant. Compound A is eluted in preference to compound B. Which of the compounds A or B, is more readily adsorbed on the column? Solution: Compound A doesnt adsorb on the column well and moves down the column with alcohol (eluant), while compound B gets adsorbed well on the column and cannot move down....
Read More →The purest form of iron is prepared by oxidising
Question: The purest form of iron is prepared by oxidising impurities from cast iron in a reverberatory furnace. Which iron ore is used to line the furnace? Explain by giving a reaction. Solution: Haematite ore (Fe2O3) is the iron ore used to line the reverberatory furnace. Fe2O3 + 3 C 2 Fe + 3CO Haematite is reduced by coke to wrought iron and the coke gets oxidised to CO....
Read More →How do we separate two sulphide
Question: How do we separate two sulphide ores by Froth Floatation Method? Explain with an example. Solution: Two sulphide ores competing to come to the froth can be separated by adjusting the oil to water proportion or by adding a depressant like NaCN. If we have two sulphide ores, ZnS and PbS, NaCN will prevent ZnS from coming to the froth and instead PbS will form the froth. This way the two ores can be separated....
Read More →Show that the function
Question: Show that the function (i) $f: N \rightarrow N: f(x)=x^{3}$ is one - one into (ii) $f: Z \rightarrow Z: f(x)=x^{3}$ is one - one into Solution: (i) $f: N \rightarrow N: f(x)=x^{3}$ is one - one into. $f(x)=x^{3}$ Since the function f(x) is monotonically increasing from the domain N N $\therefore f(x)$ is one -one Range of $f(x)=(-\infty, \infty) \neq N$ (codomain) $\therefore f(x)$ is into $\therefore f: N \rightarrow N: f(x)=x^{2}$ is one - one into. (ii) $f: Z \rightarrow Z: f(x)=x^{...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \cos ^{-1}\left(4 x^{3}-3 x\right) d x$ Solution: Let $I=\int \cos ^{-1}\left(4 x^{3}-3 x\right) d x$ $x=\cos \theta \Rightarrow d x=-\sin \theta d \theta$ $I=-\int \cos ^{-1}\left(4 \cos ^{3} \theta-3 \cos \theta\right) \sin \theta d \theta$ We know that, $\left(4 \cos ^{3} \theta-3 \cos \theta\right)=\cos 3 \theta$ $=-\int \cos ^{-1}(\cos 3 \theta) \sin \theta d \theta$ $=-\int 3 \theta \sin \theta d \theta$ Using integration by parts, $=-3\lef...
Read More →Although carbon and hydrogen are better-reducing
Question: Although carbon and hydrogen are better-reducing agents they are not used to reduce metallic oxides at high temperatures. Why? Solution: Carbon and hydrogen will not reduce oxides to metals but they will instead form hydrides and carbides. Therefore, they are not used as reducing agents....
Read More →How is copper extracted from
Question: How is copper extracted from low-grade copper ores? Solution: Copper is extracted by hydrometallurgy from low-grade copper ores. Cu is treated with scrap iron or H2. It is leached out with acid. Cu2+(aq) + H2(g) Cu(s) + 2H+(aq) 31. Write two basic requirements for refining of metal by Mond process and by Van Arkel Method. Solution: (i) The metal should react easily with the reagent to form the complex. (ii) The volatile complex should easily decompose and not give any side products and...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: Solution: Let $I=\int \frac{x^{2} \tan ^{-1} x}{1+x^{2}} d x$ $\tan ^{-1} \mathrm{x}=\mathrm{t} ; \mathrm{x}=\operatorname{tant} \int \frac{\mathrm{x}^{2} \tan ^{-1} \mathrm{x}}{1+\mathrm{x}^{2}} \mathrm{dx}$ $\frac{1}{1+x^{2}} d x=d t$ $I=\int t \tan ^{2} t d t$ We know that, $\tan ^{2} \mathrm{t}=\sec ^{2} \mathrm{t}-1$ $=\int \mathrm{t}\left(\sec ^{2} \mathrm{t}-1\right) \mathrm{dt}$ $=\int \mathrm{tsec}^{2} \mathrm{t} \mathrm{dt}-\int \mathrm{tdt}$...
Read More →Wrought iron is the purest form of iron.
Question: Wrought iron is the purest form of iron. Write a reaction used for the preparation of wrought iron from cast iron. How can the impurities of sulphur, silicon and phosphorus be removed from cast iron? Solution: Fe2O3 + 3 C 2 Fe + 3CO Limestone is added as a flux to remove the impurities of sulphur, silicon and phosphorous. They form a slag which can be easily removed. The metal is removed from the slag by passing through rollers....
Read More →At temperatures above 1073K
Question: At temperatures above 1073K coke can be used to reduce FeO to Fe. How can you justify this reduction with the Ellingham diagram? Solution: The ∆G for the formation of FeO is less negative than ∆G for the formation of carbon monoxide from carbon. The summation of both the ∆G will be negative about 1073K. Above 1073K the line for the formation of FeO lies above the line for the oxidation of C to CO. So, in this range, coke will be reducing the FeO and will itself be oxidised to CO. FeO +...
Read More →Show that the function
Question: Show that the function (i) $f: N \rightarrow N: f(x)=x^{2}$ is one - one into. (ii) $f: Z \rightarrow Z: f(x)=x^{2}$ is many - one into Solution: (i) $f: N \rightarrow N: f(x)=x^{2}$ is one - one into. $f(x)=x^{2}$ $\Rightarrow y=x^{2}$ Since the function $f(x)$ is monotonically increasing from the domain $N \rightarrow N$ $\therefore f(x)$ is one -one Range of $f(x)=(0, \infty) \neq N($ codomain $)$ $\therefore f(x)$ is into $\therefore f: N \rightarrow N: f(x)=x^{2}$ is one - one int...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{\sin ^{-1} x}{x^{2}} d x$ Solution: Let $I=\int \frac{\sin ^{-1} x}{x^{2}} d x$ $=\int \frac{1}{x^{2}} \sin ^{-1} x d x$ Using integration by parts, $I=\left[\sin ^{-1} x \times \int \frac{1}{x^{2}}-\int\left(\frac{1}{\sqrt{1-x^{2}}}\right) \int \frac{1}{x^{2}} d x\right] d x$ $=\sin ^{-1} x\left(\frac{-1}{x}\right)-\int \frac{1}{\sqrt{1-x^{2}}}\left(\frac{-1}{x}\right) d x$ $I=\frac{-1}{x} \sin ^{-1} x+\int \frac{1}{x \sqrt{1-x^{2}}} d x$ ...
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