On adding a drop of barium chloride solution
Question: On adding a drop of barium chloride solutionto an aqueous solution of sodium sulphite, white precipitate is obtained : (a) Write a balanced chemical equation for the reaction involved. (b) What other name can be given to this precipitation reaction ? (c) On adding dilute hydrochloric acid to the reaction mixture, white precipitate disappears. Why ? Solution: $\begin{aligned} \text { (a) } \mathrm{BaCl}_{2}(a q)+\mathrm{Na}_{2} \mathrm{SO}_{3}(a q) \longrightarrow \mathrm{BaSO}_{3}(s)+2...
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Question: If prove that $\frac{d}{d x}\left\{\frac{x}{2} \sqrt{a^{2}-x^{2}}+\frac{a^{2}}{2} \sin ^{-1} \frac{x}{a}\right\}=\sqrt{a^{2}-x^{2}}$. Solution: Let $y=\frac{x}{2} \sqrt{a^{2}-x^{2}}+\frac{a^{2}}{2} \sin ^{-1} \frac{x}{a}$ On differentiating $y$ with respect to $x$, we get $\frac{d y}{d x}=\frac{d}{d x}\left(\frac{x}{2} \sqrt{a^{2}-x^{2}}+\frac{a^{2}}{2} \sin ^{-1} \frac{x}{a}\right)$ $\Rightarrow \frac{d y}{d x}=\frac{1}{2}\left[\frac{d}{d x}\left(x \sqrt{a^{2}-x^{2}}+a^{2} \sin ^{-1} ...
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Question: Solve: $m-\frac{(m-1)}{2}=1-\frac{(m-2)}{3}$ Solution: $m-\frac{(m-1)}{2}=1-\frac{(m-2)}{3}$ $\Rightarrow \frac{2 m-m+1}{2}=1-\frac{(m-2)}{3} \quad($ L.C.M. of 1 and 2 is 2$)$ $\Rightarrow \frac{m+1}{2}=\frac{3-m+2}{3} \quad(L . C . M .$ of 1 and 3 is 3$)$ $\Rightarrow \frac{m+1}{2}=\frac{5-m}{3}$ $\Rightarrow 3(m+1)=2(5-m) \quad \quad$ (by cross multiplication) $\Rightarrow 3 m+3=10-2 m$ $\Rightarrow 3 m+2 m=10-3$ $\Rightarrow 5 m=7$ $\Rightarrow m=\frac{7}{5}$ $\therefore m=\frac{7}{...
Read More →What happens when zinc granules are
Question: What happens when zinc granules are treated with dilute solution of H2SO4, HCl, HNO3, NaCl and NaOH ? Also write the chemical equations if reaction ocurs. Solution: With dilute H2SO4: Hydrogen gas evolves Zn (s) + H2SO4(dil.) ZnSO4(aq) + H2(g) with dilute HCl : Hydrogen gas evolves Zn (s) + 2HCl (dil.) ZnCl2(aq) + H2(g) with dilute HNO3: Nitrous oxide gas evolves. It is colourless. 4Zn (s) + 10HNO3(aq) - 4Zn(NO3)2(aq) + 5H2O (l) + N2O(g) with NaCl : There is no chemical reaction, with ...
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Question: Solve: $m-\frac{(m-1)}{2}=1-\frac{(m-2)}{3}$ Solution: $m-\frac{(m-1)}{2}=1-\frac{(m-2)}{3}$ $\Rightarrow \frac{2 m-m+1}{2}=1-\frac{(m-2)}{3} \quad($ L.C.M. of 1 and 2 is 2$)$ $\Rightarrow \frac{m+1}{2}=\frac{3-m+2}{3}$ ($ L.C.M. of 1 and 3 is 3$)$ $\Rightarrow \frac{m+1}{2}=\frac{5-m}{3}$ $\Rightarrow 3(m+1)=2(5-m) \quad \quad$ (by cross multiplication) $\Rightarrow 3 m+3=10-2 m$ $\Rightarrow 3 m+2 m=10-3$ $\Rightarrow 5 m=7$ $\Rightarrow m=\frac{7}{5}$ $\therefore m=\frac{7}{5}$...
Read More →What happens when a piece of
Question: What happens when a piece of (a) zinc metal is added to copper sulphate solution ? (b) aluminium metal is added to dilute hydrochloric acid ? (c) silver metal is added to copper sulphate solution ? Also write the balanced chemical equation if the reaction occurs. Solution: (a) Metal zinc displaces hydrogen component on reacting with dilute sulphuric acid (H2SO4) as H2gas which is evolved Zn(s) + H2SO2(aq) - ZnSO4(aq) + H2(g) (b) Ammonia and hydrogen chloride gas. When vapours of ammoni...
Read More →Give the characteristic tests for the following gases :
Question: Give the characteristic tests for the following gases : (a)CO2 (b)SO2 (c)O2 (d)H2 Solution: (a)CO2gas : It is a colourless and odourless gas. When passed through lime water, it will initially become milky. (b)SO2gas : It is a colourless but a pungent smelling gas. The gas when passed through an acidified solution of potassium permanganate (pink) will decolourise it. Similarly the gas when passed through an acidified solution of potassium dichromate (orange) will make it light green. (c...
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Question: If $x y=4$, prove that $x\left(\frac{d y}{d x}+y^{2}\right)=3 y$. Solution: Given $x y=4$ $\Rightarrow y=\frac{4}{x}$ On differentiating y with respect to $x$, we get $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{d}}{\mathrm{dx}}\left(\frac{4}{\mathrm{x}}\right)$\ $\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=4 \frac{\mathrm{d}}{\mathrm{dx}}\left(\frac{1}{\mathrm{x}}\right)$ $\Rightarrow \frac{d y}{d x}=4 \frac{d}{d x}\left(x^{-1}\right)$ We know $\frac{d}{d x}\left(x^{n}\right)=n x^{n...
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Question: Solve: $\frac{2 x-(7-5 x)}{9 x-(3+4 x)}=\frac{7}{6}$ Solution: $\frac{2 x-(7-5 x)}{9 x-(3+4 x)}=\frac{7}{6}$ $\Rightarrow \frac{2 x-7+5 x}{9 x-3-4 x}=\frac{7}{6}$ $\Rightarrow \frac{7 x-7}{5 x-3}=\frac{7}{6}$ $\Rightarrow 6(7 x-7)=7(5 x-3)$ (by cross multiplication) $\Rightarrow 42 x-42=35 x-21$ $\Rightarrow 42 x-35 x=42-21$ $\Rightarrow 7 x=21$ $\Rightarrow x=\frac{21}{7}=3$ $\therefore x=3$...
Read More →On heating blue coloured powder of copper (II) nitrate,
Question: On heating blue coloured powder of copper (II) nitrate, in a boiling tube, copper oxide (black), oxygen gas and a brown gas X is formed (a) Write a balanced chemical equation of the reaction. (b) Identify the brown gas X evolved. (c) Identify the type of reaction. (d) What could be the pH range of aqueous solution of the gas X ? Solution: (b) Brown gas (X) is nitrogen dioxide. (c) It is an example of decomposition reaction. (d) Nitrogen dioxide is an acidic oxide. Therefore, it dissolv...
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Question: Solve: $\frac{15(2-y)-5(y+6)}{1-3 y}=10$ Solution: $\frac{15(2-y)-5(y+6)}{1-3 y}=10$ $\Rightarrow \frac{30-15 y-5 y-30}{1-3 y}=10$ $\Rightarrow \frac{-20 y}{1-3 y}=10$ $\Rightarrow 1(-20 y)=10(1-3 y)$ (by cross multiplication) $\Rightarrow-20 y=10-30 y$ $\Rightarrow-20 y+30 y=10$ $\Rightarrow 10 y=10$ $\Rightarrow y=\frac{10}{10}=1$ $\therefore y=1$...
Read More →A silver article generally turns black
Question: A silver article generally turns black when kept in the open for a few days. The article when rubbed with toothpaste again starts shining. (a) Why do silver articles turn black when kept in the open for a few days ? Name the phenomenon involved. (b) Name the black substance formed and give its chemical formula. Solution: (a) Air contains traces of hydrogen sulphide (H2S) gas. It slowly reacts with silver present in the silver article to form silver sulphide (black in colour). A coating...
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Question: Solve: $\frac{7 y+4}{y+2}=\frac{-4}{3}$ Solution: $\frac{7 y+4}{y+2}=\frac{-4}{3}$ $\Rightarrow 3(7 y+4)=-4(y+2)$ (by cross multiplication) $\Rightarrow 21 y+12=-4 y-8$ $\Rightarrow 21 y+4 y=-8-12$ $\Rightarrow 25 y=-20$ $\Rightarrow y=\frac{-20}{25}=\frac{-4}{5}$ $\therefore y=\frac{-4}{5}$...
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Question: If $y=\sqrt{a^{2}-x^{2}}$, prove that $y \frac{d y}{d x}+x= 0$ Solution: Given $y=\sqrt{a^{2}-x^{2}}$ On differentiating $y$ with respect to $x$, we get $\frac{d y}{d x}=\frac{d}{d x}\left(\sqrt{a^{2}-x^{2}}\right)$ $\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{d}}{\mathrm{dx}}\left[\left(\mathrm{a}^{2}-\mathrm{x}^{2}\right)^{\frac{1}{2}}\right]$ We know $\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{x}^{\mathrm{n}}\right)=\mathrm{n} \mathrm{x}^{\mathrm{n}-1}$ $\Rightarrow \...
Read More →Zinc liberates hydrogen gas
Question: Zinc liberates hydrogen gas when reacted with dilute hydrochloric acid whereas copper does not. Explain why ? Solution: Zinc (Zn) is placed above hydrogen in the activity series. It therefore, displaces hydrogen from dilute HCl. Zn (s) + 2HCl (aq) - ZnCl2(aq) + H2(g) Copper is placed below hydrogen and therefore, does not react with dilute HCl. Cu (s) + HCl (aq) No action....
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Question: Solve: $\frac{4 x+7}{9-3 x}=\frac{1}{4}$ Solution: $\frac{4 x+7}{9-3 x}=\frac{1}{4}$ $\Rightarrow 4(4 x+7)=1(9-3 x) \quad$ (by cross multiplication) $\Rightarrow 16 x+28=9-3 x$ $\Rightarrow 16 x+3 x=9-28$ $\Rightarrow 19 x=-19$ $\Rightarrow x=\frac{-19}{19}=-1$ $\therefore x=-1$...
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Question: Solve: $\frac{2-9 z}{17-4 z}=\frac{4}{5}$ Solution: $\frac{2-9 z}{17-4 z}=\frac{4}{5}$ $\Rightarrow 5(2-9 z)=4(17-4 z) \quad$ (by cross multiplication) $\Rightarrow 10-45 z=68-16 z$ $\Rightarrow 10-68=45 z-16 z$ $\Rightarrow-58=29 z$ $\Rightarrow 29 z=-58 \quad$ (by transposition) $\Rightarrow z=\frac{-58}{29}=-2$ $\therefore z=-2$...
Read More →A magnesium ribbon is burnt in oxygen
Question: A magnesium ribbon is burnt in oxygen to give a white compound X accompanied by emission of light. If the burning ribbon is now placed in an atmosphere of nitrogen, it continues to burn and forms a compound Y. (a) Write the chemical formulae of X and Y. (b) Write a balanced chemical equations when X and Y are dissolved in water. Solution: (a) The Compound X is magnesium oxide (MgO). The compound Y is magnesium nitride (Mg3N2) (b) $\mathrm{MgO}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longright...
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Question: Solve: $\frac{6 y-5}{2 y}=\frac{7}{9}$ Solution: $\frac{6 y-5}{2 y}=\frac{7}{9}$ $\Rightarrow 9(6 y-5)=7(2 y) \quad$ (by cross multiplication) $\Rightarrow 54 y-45=14 y$ $\Rightarrow 54 y-14 y=45$ $\Rightarrow 40 y=45$ $\Rightarrow y=\frac{45}{40}=\frac{9}{8}$ $\therefore y=\frac{9}{8}$...
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Question: If $y=e^{x}+e^{-x}$, prove that $\frac{d y}{d x}=\sqrt{y^{2}-4} .$ Solution: Given $y=e^{x}+e^{-x}$ On differentiating $y$ with respect to $x$, we get $\frac{d y}{d x}=\frac{d}{d x}\left(e^{x}+e^{-x}\right)$ $\Rightarrow \frac{d y}{d x}=\frac{d}{d x}\left(e^{x}\right)+\frac{d}{d x}\left(e^{-x}\right)$ We know $\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{e}^{\mathrm{x}}\right)=\mathrm{e}^{\mathrm{x}}$ $\Rightarrow \frac{d y}{d x}=e^{x}+e^{-x} \frac{d}{d x}(-x)$ [using chain rule] $\Righ...
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Question: Solve: $\frac{3 x}{5 x+2}=-4$ Solution: $\frac{3 x}{5 x+2}=-4$ $\Rightarrow \frac{3 x}{5 x+2}=\frac{-4}{1}$ $\Rightarrow 1(3 x)=-4(5 x+2)$ (by cross multiplication) $\Rightarrow 3 x=-20 x-8$ $\Rightarrow 3 x+20 x=-8$ $\Rightarrow 23 x=-8$ $\Rightarrow x=\frac{-8}{23}$ $\therefore x=\frac{-8}{23}$...
Read More →Balance the following chemical
Question: Balance the following chemical equations and identify the type of chemical reaction. (a) $\quad \mathrm{Mg}(s)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{MgCl}_{2}(s)$ (b) $\quad \mathrm{HgO}(s) \stackrel{\text { theat })}{\longrightarrow} \mathrm{Hg}(l)+\mathrm{O}_{2}(g)$ (c) $\quad \mathrm{Na}(s)+\mathrm{S}(s) \stackrel{\text { (Fuse) }}{\longrightarrow} \mathrm{Na}_{2} \mathrm{~S}(s)$ (d) $\mathrm{TiCl}_{4}(l)+\mathrm{Mg}(s) \longrightarrow \mathrm{Ti}(s)+\mathrm{MgCl}_{2}(s)$ (e) $...
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Question: Solve: $\frac{9 x}{7-6 x}=15$ Solution: $\frac{9 x}{7-6 x}=15$ $\Rightarrow \frac{9 x}{7-6 x}=\frac{15}{1}$ $\Rightarrow 1(9 x)=15(7-6 x) \quad$ (by cross multiplication) $\Rightarrow 9 x=105-90 x$ $\Rightarrow 9 x+90 x=105$ $\Rightarrow 99 x=105$ $\Rightarrow x=\frac{105}{99}=\frac{35}{33}$ $\therefore x=\frac{35}{33}$...
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Question: Solve: $\frac{8 x-3}{3 x}=2$ Solution: $\frac{8 x-3}{3 x}=2$ $\Rightarrow 8 x-3=2(3 x) \quad($ by cross multiplication $)$ $\Rightarrow 8 x-3=6 x$ $\Rightarrow 8 x-6 x=3$ $\Rightarrow 2 x=3$ $\Rightarrow x=\frac{3}{2}$ $\therefore x=\frac{3}{2}$...
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Question: If $y=\sqrt{x^{2}+a^{2}}$, prove that $y \frac{d y}{d x}-x=0$ Solution: Given $y=\sqrt{x^{2}+a^{2}}$ On differentiating $y$ with respect to $x$, we get $\frac{d y}{d x}=\frac{d}{d x}\left(\sqrt{x^{2}+a^{2}}\right)$ $\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{d}}{\mathrm{dx}}\left[\left(\mathrm{x}^{2}+\mathrm{a}^{2}\right)^{\frac{1}{2}}\right]$ We know $\frac{d}{d x}\left(x^{n}\right)=n x^{n-1}$ $\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{1}{2}\left(\mathrm{x}^{2}+...
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