Match the species given in Column I with
Question: Match the species given in Column I with the properties mentioned in Column II. Solution: (i) is e (ii) is c (iii) is d (iv) is a,b...
Read More →Complete the following chemical equations :
Question: Complete the following chemical equations : Z + 3 LiAiH4 X + 3 Lif + 3AIF3 3X + 3O2 B2O3+ 3H2O Solution: BF3+ 3LiAlH4 B2H6+ 3LiF + 3AlF3 3B2H6+ 3O2 B2O3+ 3H2O...
Read More →Identify the compounds A,
Question: Identify the compounds A, X and Z in the following reactions : (i) A + 2HCL + 5H2O 2NaCI + X X HBO2 Z Solution: A is Borax which reacts with HCl in the presence of water to give Orthoboric acid(X). Upon heating Orthoboric acid Gives metaboric and further on heating gives the compound Z i.e. Boron trioxide....
Read More →Find the equation of the line whose inclination is
Question: Find the equation of the line whose inclination is $\frac{5 \pi}{6}$ and which makes an intercept of 6 units on the negative direction of the y - axis. Solution: Given: $\theta=\frac{5 \pi}{6}$ $\therefore$ slope, $m=\tan \theta=\tan \frac{5 \pi}{6}=-\frac{1}{\sqrt{3}}$ The y - intercept is 6 units. Formula to be used: y = mx + c where m is the slope of the line and c is the y - intercept. The equation of the line is $y=-\frac{1}{\sqrt{3}} x-6$ i.e. $\sqrt{3} y+x+6 \sqrt{3}=0$...
Read More → Explain the following :
Question: Explain the following : (i) Gallium has a higher ionisation enthalpy than aluminium. (ii) Boron does not exist as B3+ ion. (iii) Aluminium forms [AlF6]3- ion but boron does not form [BF6]3- ion. (iv) PbX2 is more stable than PbX4. (v) Pb4+ acts as an oxidising agent but Sn2+ acts as a reducing agent. (vi) Electron gain enthalpy of chlorine is more negative as compared to fluorine. (vii) Tl (NO3)3 acts as an oxidising agent. (viii) Carbon shows catenation property but lead does not. (ix...
Read More →Prove that
Question: Prove that $f(x)=a x+b$, where $a$, $b$ are constants and $a0$ is an increasing function on $R$. Solution: we have, $f(x)=a x+b, a0$ let $x_{1}, x_{2} \in R$ and $x_{1}x_{2}$ $\Rightarrow \mathrm{ax}_{1}\mathrm{ax}_{2}$ for some $\mathrm{a}0$ $\Rightarrow \mathrm{ax}_{1}+\mathrm{b}\mathrm{ax}_{2}+\mathrm{b}$ for some $\mathrm{b}$ $\Rightarrow \mathrm{f}\left(\mathrm{x}_{1}\right)\mathrm{f}\left(\mathrm{x}_{2}\right)$ Hence, $x_{1}x_{2} \Rightarrow f\left(x_{1}\right)f\left(x_{2}\right)...
Read More →Aluminium dissolves in mineral acids and aqueous
Question: Aluminium dissolves in mineral acids and aqueous alkalies and thus shows amphoteric character. A piece of aluminium foil is treated with dilute hydrochloric acid or dilute sodium hydroxide solution in a test tube and on bringing a burning matchstick near the mouth of the test tube, a pop sound indicates the evolution of hydrogen gas. The same activity when performed with concentrated nitric acid, the reaction doesnt proceed. Explain the reason. Solution: Aluminium reacts both with acid...
Read More →When BCl3 is treated with water,
Question: When BCl3 is treated with water, it hydrolyses and forms [B[OH]4]- only whereas AlCl3 in acidified aqueous solution forms [Al (H2O)6]3+ ion. Explain what is the hybridisation of boron and aluminium in these species? Solution: AlCl3+ 6H2O [Al(H2O)6]3++ 3Cl The 6 H2O molecules get attach with Al i.e. donate 6 electron pair to the 3s,3p and 3d orbital of Al3+ ion. Thus, the hybridization of the Al atom in [Al(H2O)6]3+species is sp3d2....
Read More →Prove that the function
Question: Prove that the function $f(x)=\log _{a} x$ is increasing on $(0, \infty)$ if $a1$ and decresing on $(0, \infty)$, if $0a1$. Solution: case I When $a1$ let $x_{1}, x_{2} \in(0, \infty)$ We have, $x_{1}x_{2}$ $\Rightarrow \log _{\mathrm{e}} \mathrm{x}_{1}\log _{\mathrm{e}} \mathrm{x}_{2}$ $\Rightarrow \mathrm{f}\left(\mathrm{x}_{1}\right)\mathrm{f}\left(\mathrm{x}_{2}\right)$ So, $f(x)$ is increasing in $(0, \infty)$ case II When $0a1$ $f(x)=\log _{a} x=\frac{\log x}{\log a}$ when $a1 \R...
Read More →If a trivalent atom replaces a few silicon atoms
Question: If a trivalent atom replaces a few silicon atoms in a three-dimensional network of silicon dioxide, what would be the type of charge on an overall structure? Solution: If a few tetrahedral Si atoms in a three-dimensional network structure of SiO2 are replaced by an equal number of trivalent atoms, then one valence electron of each Si atom will become free. As a result, the substitution of each Si atom by a trivalent atom will introduce one unit negative charge into the three-dimensiona...
Read More →Find the equation of the line which makes an angle of
Question: Find the equation of the line which makes an angle of $30^{\circ}$ with the positive direction of the x - axis and cuts off an intercept of 4 units with the negative direction of the y - axis. Solution: Given : The given line makes an angle of $30^{\circ}$ with the $x$-axis. The $y$-intercept $=-4$. So, the slope of the line is $m=\tan \theta=\tan 30^{\circ}=1 / \sqrt{3}$. Formula to be used: $y=m x+c$ where $m$ is the slope of the line and $c$ is the $y-$ intercept. The equation of th...
Read More →Carbon and silicon both belong to the group 14,
Question: Carbon and silicon both belong to the group 14, but despite the stoichiometric similarity, the dioxides, (i.e., carbon dioxide and silicon dioxide), differ in their structures. Comment. Solution: Carbon can form stable p-p bonding with itself and other small atoms like oxygen and nitrogen due to its small size. it carbon dioxide each oxygen atom is double- bonded with the carbon atom with p-p overlapping. Silicon cannot form this bonding because of its large size....
Read More →The +1 oxidation state in group 13 and +2
Question: The +1 oxidation state in group 13 and +2 oxidation state in group 14 becomes more and more stable with increasing atomic number. Explain. Solution: Due to the poor shielding of s orbital electrons by d and f orbitals, the tendency of s orbital to form the bond and will decreases down the group from group 13 and 14. This property is called the inner pair effect. Thus, the +1 oxidation state in group 13 and +2 oxidation state in group 14 becomes more and more stable with increasing atom...
Read More →Explain the following :
Question: Explain the following : (i) CO2 is a gas whereas SiO2 is solid. (ii) Silicon forms SiF62- ion whereas the corresponding fluoro compound of carbon is not known. Solution: (i) Silicon has a large size compared to carbon. It does not form good overlapping. It forms four single covalent bonds with oxygen atoms. Each oxygen atom is linked with two Si atoms. Thus, a large giant molecule of a 3-d structure is formed whereas carbons form a double bond with oxygen atom due to overlapping. (ii) ...
Read More →Find the equation of the line whose
Question: Find the equation of the line whose (i) slope $=3$ and $y-$ intercept $=5$ (ii) slope $=-1$ and $y$ - intercept $=4$ (iii) slope $=-\frac{2}{5}$ and $y-$ intercept $=-3$ Solution: (i) Formula to be used: y = mx + c where m is the slope of the line and c is the y - intercept Here, m = 3 and c = 5. Hence, y = (3)x + (5) i.e. y = 3x + 5 (ii) Formula to be used: y = mx + c where m is the slope of the line and c is the y - intercept. Here, m = - 1 and c = 4. Hence, y = ( - 1)x + (4) i.e. x ...
Read More →Prove that the function
Question: Prove that the function $f(x)=\log _{e} x$ is increasing on $(0, \infty)$. Solution: let $x_{1}, x_{2} \in(0, \infty)$ We have, $x_{1}x_{2}$ $\Rightarrow \log _{e} x_{1}\log _{e} x_{2}$ $\Rightarrow f\left(x_{1}\right)f\left(x_{2}\right)$ So, $f(x)$ is increasing in $(0, \infty)$...
Read More →Explain why the following compounds behave as Lewis acids?
Question: Explain why the following compounds behave as Lewis acids? (i) BCl3 (ii) AlCl3 Solution: (i) BCL3 is an electron-deficient compound because it has 6 electrons in its outermost orbital and a vacant p orbital. Hence, it acts as Lewis acid and accepts a lone pair of electrons. (ii) AlCl3 forms a covalent bond with chlorine by forming three single bonds of chlorine as aluminium has three electrons in its valence shell and act as an electron-deficient compound and act as lewis acid. 26. Giv...
Read More →Explain the nature of boric acid
Question: Explain the nature of boric acid as a Lewis acid in water. Solution: Boric acid is a weak monobasic acid and acts as a Lewis acid by accepting electrons from a hydroxyl ion. B(OH)3+ 2H2O [B(OH)4]+ H3O+ OH- is accepted by the Boric acid and the formation of hydroxyl ion takes place. Thus, Boric acid act as a Lewis acid in water....
Read More →Identify the correct resonance structures
Question: Identify the correct resonance structures of carbon dioxide from the ones given below : (i) O C O (ii) O = C = O (iii) O C O+ (iv) O C O+ Solution: Option (ii) O = C = O and (iv)O C O+ are the answers....
Read More →Solve this
Question: If $A(1,4), B(2,-3)$ and $C(-1,-2)$ are the vertices of a $\triangle A B C$, find the equation of (i) the median through $\mathrm{A}$ (ii) the altitude through A (iii) the perpendicular bisector of BC Solution: Construction: Draw a line segment from vertex A intersecting BC at the midpoint (D). (i) Equation of median AD, we will find the midpoint of side BC For side $\mathrm{BC}$ (midpoint $\mathrm{D}):(\mathrm{x}, \mathrm{y})=\frac{2+(-1)}{2}, \frac{-3+(-2)}{2}$ $(\mathrm{x}, \mathrm{...
Read More →Which of the following statements are correct?
Question: Which of the following statements are correct? (i) Fullerenes have dangling bonds (ii) Fullerenes are cage-like molecules (iii) Graphite is a thermodynamically most stable allotrope of carbon (iv) Graphite is slippery and hard and therefore used as a dry lubricant in Machines Solution: Option (ii) and (iii) are the answers....
Read More →Me3SiCl is used during polymerisation
Question: Me3SiCl is used during polymerisation of organic silicones because (i) the chain length of organic silicone polymers can be controlled by adding Me3SiCl (ii) Me3SiCl blocks the end terminal of a silicone polymer (iii) Me3SiCl improves the quality and yield of the polymer (iv) Me3SiCl acts as a catalyst during polymerisation Solution: Option (i) and (ii) are the answers....
Read More →The linear shape of CO2 is due to _________.
Question: The linear shape of CO2 is due to _________. (i) sp3 hybridisation of carbon (ii) sp hybridisation of carbon (iii) p p bonding between carbon and oxygen (iv) sp2 hybridisation of carbon Solution: Option (ii) and (iii) are the answers....
Read More →The reason for the small radius of Ga compared to Al is _______.
Question: The reason for the small radius of Ga compared to Al is _______. (i) poor screening effect of d and f orbitals (ii) increase in nuclear charge (iii) presence of higher orbitals (iv) higher atomic number Solution: Option (i)poor screening effect of d and f orbitals and (ii)increase in nuclear charge are the answers....
Read More →Write the equation of the tangent drawn to the curve
Question: Write the equation of the tangent drawn to the curve $y=\sin x$ at the point $(0,0)$. Solution: Given that $y=\sin x$ The slope of the tangent: $\frac{d y}{d x}=\cos x$ For origin $(a, b)$ slope $=\cos 0=1$ Equation of the tangent: $\left(y-y_{1}\right)=$ Slope of tangent $\times\left(x-x_{1}\right)$ So, the equation of the tangent at the point $(0,0)$ $y-0=1(x-0)$ $\Rightarrow y=x$...
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