Why is an external emf of more than 2.2V
Question: Why is an external emf of more than 2.2V required for the extraction of Cl2 from brine? Solution: 2Cl (aq) + 2H2O(l) 2OH (aq) + H2(g) + Cl2(g) The ΔGᶱ for this reaction is +422kJmol-1. Using the formula, ΔGᶱ = -nFE E = 422 x 103/296500 we get = -2.2V For the reaction to take place the external voltage should be greater than 2.2V otherwise the reaction will not happen....
Read More →Prove that
Question: Let $f:\left[0, \frac{\pi}{2}\right] \rightarrow R: f(x)=\sin x$ and $g:\left[0, \frac{\pi}{2}\right] \rightarrow R: g(x)=\cos x$ Show that each one of $f$ and $g$ is one - one but $(f+g)$ is not one - one. Solution: $f:\left[0, \frac{\pi}{2}\right] \rightarrow R: f(x)=\sin x$ Here in this range, the lines do not cut the curve in 2 equal valued points of $y$, therefore, the function $f(x)=$ $\sin x$ is one - one. $g:\left[0, \frac{\pi}{2}\right] \rightarrow R: g(x)=\cos x$ in this rang...
Read More →In the extraction of chlorine from
Question: In the extraction of chlorine from brine _____________. A. ΔG for the overall reaction is negative. B. ΔG for the overall reaction is positive. C. E for the overall reaction has a negative value. D. E for the overall reaction has a positive value. Solution: Option (ii) and (iii) are the answers....
Read More →Which of the following statements are correct?
Question: Which of the following statements are correct? (i) A depressant prevents a certain type of particle to come to the froth. (ii) Copper matte contains Cu2S and ZnS. (iii) The solidified copper obtained from the reverberatory furnace has blistered appearance due to evolution of SO2 during the extraction. (iv) Zinc can be extracted by self-reduction. Solution: Option (i) and (iii) are the answers....
Read More →In which of the following method of purification,
Question: In which of the following method of purification, metal is converted to its volatile compound which is decomposed to give pure metal? (i) heating with a stream of carbon monoxide. (ii) heating with iodine. (iii) liquation. (iv) distillation. Solution: Option (i) and (ii) are the answers....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int x^{2} \sin ^{-1} x d x$ Solution: Let $I=\int x^{2} \sin ^{-1} x d x$ Using integration by parts, $I=\sin ^{-1} x \int x^{2} d x-\int \frac{d}{d x} \sin ^{-1} x \int x^{2} d x$ $=\frac{x^{3}}{3} \sin ^{-1} x-\int \frac{x^{3}}{3 \sqrt{1-x^{2}}} d x$ $I=\frac{x^{3}}{3} \sin ^{-1} x-\int I_{1}+C$ .......(i) $\mathrm{I}_{1}=-\int \frac{\mathrm{x}^{3}}{3 \sqrt{1-\mathrm{x}^{2}}} \mathrm{dx}$ Let $1-x^{2}=t^{2}$ $-2 x d x=2 t d t$ $-x d x=t d t$ $\math...
Read More →The main reactions occurring in the blast
Question: The main reactions occurring in the blast furnace during the extraction of iron from haematite are ________. (i) Fe2O3 + 3CO 2Fe + 3CO2 (ii) FeO + SiO2 FeSiO3 (iii) Fe2O3 + 3C 2Fe + 3CO (iv) CaO + SiO2 CaSiO3 Solution: Option (i) and (iv) are the answers...
Read More →For the metallurgical process
Question: For the metallurgical process of which of the ores calcined ore can be reduced by carbon? (i) haematite (ii) calamine (iii) iron pyrites (iv) sphalerite Solution: Option (i) and (ii) are the answers....
Read More →Which of the following reactions occur
Question: Which of the following reactions occur during calcination? (i) CaCO3 CaO + CO2 (ii) 2FeS2 + 11/2 O2 Fe2O3 + 4SO2 (iii) Al2O3.x H2O Al2O3 + x H2O (iv) ZnS + 3/2O2 ZnO + SO2 Solution: Option (i) and (iii) are the answers....
Read More →Which of the following ores are
Question: Which of the following ores are concentrated by froth flotation? (i) Haematite (ii) Galena (iii) Copper pyrites (iv) Magnetite Solution: Option (ii) and (iii) are the answers....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \tan ^{-1}\left(\frac{3 x-x^{3}}{1-3 x^{2}}\right) d x$ Solution: Let $\mathrm{I}=\int \tan ^{-1}\left(\frac{3 \mathrm{x}-\mathrm{x}^{2}}{1-3 \mathrm{x}^{2}}\right) \mathrm{dx}$ $\mathrm{x}=\tan \theta \Rightarrow \mathrm{dx}=\sec ^{2} \theta \mathrm{d} \theta$ We know that, $\frac{3 \tan \theta-\tan \theta^{3}}{1-3 \tan \theta^{2}}=\tan 3 \theta$ $\mathrm{I}=\int \tan ^{-1}\left(\frac{3 \tan \theta-\tan \theta^{3}}{1-3 \tan \theta^{2}}\right) \s...
Read More →Common impurities present in
Question: Common impurities present in bauxite are ____________. (i) CuO (ii) ZnO (iii) Fe2O3 (iv) SiO2 Solution: Option (iii) and (iv) are the answers....
Read More →Find the value
Question: Show that the function $f: R \rightarrow R: f(x)=x^{5}$ is one $-$ one and onto. Solution: To show: $f: R \rightarrow R:: f(x)=x^{5}$ is one - one and onto. Proof: $f(x)=x^{5}$ $\Rightarrow y=x^{5}$ Since the lines do not cut the curve in 2 equal valued points of $y$, therefore, the function $f(x)$ is one - one. The range of $f(x)=(-\infty, \infty)=R$ (Codomain) $\therefore f(x)$ is onto Hence, showed $f: R \rightarrow R: f(x)=x^{5}$ is one - one and onto....
Read More →In the Froth Floatation process,
Question: In the Froth Floatation process, zinc sulphide and lead sulphide can be separated by ______________. (i) using collectors. (ii) adjusting the proportion of oil to water. (iii) using depressant. (iv) using froth stabilisers. Solution: Option (ii) and (iii) are the answers....
Read More →Which of the following statements is correct
Question: Which of the following statements is correct about the role of substances added in the froth floatation process? (i) Collectors enhance the non-wettability of the mineral particles. (ii) Collectors enhance the wettability of gangue particles. (iii) By using depressants in the process two sulphide ores can be separated. (iv) Froth stabilisers decrease wettability of gangue. Solution: Option (i) and (iii) are the answers....
Read More →In the extraction of aluminium by
Question: In the extraction of aluminium by Hall-Heroult process, purified Al2O3 is mixed with CaF2 to (i) lower the melting point of Al2O3 (ii) increase the conductivity of molten mixture. (iii) reduce Al3+ into Al(s). (iv) acts as a catalyst Solution: Option (i) and (ii) are the answers....
Read More →Which of the following option are correct?
Question: Which of the following option are correct? (i) Cast iron is obtained by remelting pig iron with scrap iron and coke using hot air blast. (ii) In the extraction of silver, silver is extracted as cationic complex. (iii) Nickel is purified by zone refining. (iv) Zr and Ti are purified by van Arkel method Solution: Option (i) and (iv) are the answers....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) d x$ Solution: Let $I=\int \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) d x$ $x=\tan \theta \Rightarrow d x=\sec ^{2} \theta d \theta$ $\sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right)=\sin ^{-1}\left(\frac{2 \tan \theta}{1+\tan ^{2} \theta}\right)=\sin ^{-1}(\sin 2 \theta)=2 \theta$ $\int \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) d x=\int 2 \theta \sec ^{2} \theta d \theta$ Using integration by parts, $=2\left...
Read More →At the temperature corresponding to
Question: At the temperature corresponding to which of the points in Fig.6.1, FeO will be reduced to Fe by coupling the reaction 2FeO 2Fe + O2 with all of the following reactions? (a) C + O2 CO2 (b) 2C + O2 2CO and (c) 2CO + O2 2 CO2 (i) Point A (ii) Point B (iii) Point D (iv) Point E Solution: Option (ii) and (iv) are the answers....
Read More →Show that the function
Question: Show that the function $f: R \rightarrow R: f(x)=x^{4}$ is many - one and into. Solution: To show: $f: R \rightarrow R: f(x)=x^{4}$ is many $-$ one into. Proof: $f(x)=x^{4}$ $\Rightarrow y=x^{4}$ Since the lines cut the curve in 2 equal valued points of $y$, therefore, the function $f(x)$ is many ones. The range of $f(x)=[0, \infty) \neq R($ Codomain $)$ $\therefore f(x)$ is not onto $\Rightarrow f(x)$ is into Hence, showed that $f: R \rightarrow R: f(x)=x^{4}$ is many - one into....
Read More →For the reduction of FeO at the temperature corresponding
Question: For the reduction of FeO at the temperature corresponding to point D, which of the following statements is correct? (i) ∆G value for the overall reduction reaction with carbon monoxide is zero. (ii) ∆G value for the overall reduction reaction with a mixture of 1 mol carbon and 1 mol oxygen is positive. (iii) ∆G value for the overall reduction reaction with a mixture of 2 mol carbon and 1 mol oxygen will be positive. (iv) ∆G value for the overall reduction reaction with carbon monoxide ...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \sin ^{-1}\left(3 x-4 x^{3}\right) d x$ Solution: Let $\int \sin ^{-1}\left(3 x-4 x^{3}\right) d x$ $x=\sin \theta$ $\mathrm{dx}=\cos \theta \mathrm{d} \theta$ $=\int \sin ^{-1}\left(3 \sin \theta-4 \sin ^{3} \theta\right) \cos \theta d \theta$ We know that $3 \sin \theta-4 \sin ^{3} \theta=\sin 3 \theta$ $=\int \sin ^{-1}(\sin 3 \theta) \cos \theta d \theta$ We know that, $\int \sin ^{-1}(\sin 3 \theta)=3 \theta$ $=\int 3 \theta \cos \theta d \t...
Read More →Show that the function
Question: Show that the function $f: R \rightarrow R: f(x)=1+x^{2}$ is many - one into. Solution: To show: $f: R \rightarrow R: f(x)=1+x^{2}$ is many - one into. Proof: $f(x)=1+x^{2}$ $\Rightarrow y=1+x^{2}$ Since the lines cut the curve in 2 equal valued points of $y$ therefore the function $f(x)$ is many one. The range of $f(x)=[1, \infty) \neq R($ Codomain $)$ $\therefore f(x)$ is not onto $\Rightarrow f(x)$ is into Hence, showed that $f: R \rightarrow R: f(x)=1+x^{2}$ is many - one into....
Read More →Below point ‘A’ FeO can ______________.
Question: Below point A FeO can ______________. (i) be reduced by carbon monoxide only. (ii) be reduced by both carbon monoxide and carbon. (iii) be reduced by carbon only. (iv) not be reduced by both carbon and carbon monoxide. Solution: Option (i) is the answer...
Read More →Choose the correct option of temperature at
Question: Choose the correct option of temperature at which carbon reduces FeO to iron and produces CO. (i) Below temperature at point A. (ii) Approximately at the temperature corresponding to point A. (iii) Above temperature at point A but below a temperature at point D. (iv) Above temperature at point A. Solution: Option (iv)Above temperature at point Ais the answer....
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