The ionisation of hydrochloric
Question: The ionisation of hydrochloric in water is given below: HCl(aq) + H2O (l ) ⇌ H3O+(aq) + Cl(aq) Label two conjugate acid-base pairs in this ionisation. Solution: The two conjugate acid-base pairs in the ionisation of HCl are (HCl-Cl-) in which HCl is the conjugate acid and Cl- is the conjugate base similarly the second pair is (H2O- H3O+) in which H2O is the conjugate base and H3O+ is the conjugate acid....
Read More →At a particular temperature and atmospheric pressure,
Question: At a particular temperature and atmospheric pressure, the solid and liquid phases of a pure substance can exist in equilibrium. Which of the following Does the term define this temperature? (i) Normal melting point (ii) Equilibrium temperature (iii) Boiling point (iv) Freezing point Solution: Option (i) Normal melting pointand (iv) Freezing pointare the answers....
Read More →For the reaction N2O4 (g) ⇌ 2NO2 (g),
Question: For the reaction N2O4 (g) ⇌ 2NO2 (g), the value of K is 50 at 400 K and 1700 at 500 K. Which of the following options is correct? (i) The reaction is endothermic (ii) The reaction is exothermic (iii) If NO2 (g) and N2O4 (g) are mixed at 400 K at partial pressures 20 bar and 2 bar respectively, more N2O4 (g) will be formed. (iv) The entropy of the system increases. Solution: Option (i) The reaction is endothermic (iii)If NO2 (g) and N2O4 (g) are mixed at 400 K at partial pressures 20 ba...
Read More →If the straight line
Question: If the straight line $x \cos \alpha+y \sin \alpha=p$ touches the curve $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$, then prove that $a^{2} \cos ^{2} \alpha-b^{2} \sin ^{2} \alpha=\rho^{2}$ Solution: Given: The straight line $x \cos \alpha+y \sin \alpha=p$ touches the curve $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$. Suppose the straight line $x \cos \alpha+y \sin \alpha=p$ touches the curve at $\left(x_{1}, y_{1}\right)$. But the equation of tangent to $\frac{x^{2}}{a^{2}}-\frac{y^{2}...
Read More →Show that the line through the points
Question: Show that the line through the points (5, 6) and (2, 3) is parallel to the line through the points (9, -2) and (6, -5) Solution: We know that for two lines to be parallel, their slope must be the same. Given points are $A(5,6), B(2,3)$ and $C(9,-2), D(6,-5)$ slope $=\left(\frac{\mathrm{y}_{2}-\mathrm{y}_{1}}{\mathrm{x}_{2}-\mathrm{x}_{1}}\right)$ $\Rightarrow\left(\frac{3-6}{2-5}\right)=\left(\frac{-5+2}{6-9}\right)$ $\Rightarrow\left(\frac{-3}{-3}\right)=\left(\frac{-3}{-3}\right) \Ri...
Read More →If the slope of the line joining the points A
Question: If the slope of the line joining the points $A(x, 2)$ and $B(6,-8)$ is $\frac{-5}{4}$, find the value of x. Solution: If a line passing through $\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right) \\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right)$ then slope of the line is given by slope $=\left(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\right)$ Given points are $A(x, 2)$ and $B(6,-8)$, and the slope is $\frac{-5}{4}$ $\Rightarrow\left(\frac{-8-2}{6-x}\right)=\frac{-5}{4}$ $\Rightarrow\left(\frac{-10}{6-x}\ri...
Read More →In which of the following reactions,
Question: In which of the following reactions, the equilibrium remains unaffected on addition of small amount of argon at constant volume? (i) H2 (g) + I2 (g) ⇌ 2HI (g) (ii)PCl5 (g) ⇌ PCl3 (g) + Cl2 (g) (iii) N2 (g) + 3H2 (g) ⇌ 2NH3 (g) (iv) The equilibrium will remain unaffected in all the three cases. Solution: Option (iv)The equilibrium will remain unaffected in all the three cases. is the answer....
Read More →At 500 K, the equilibrium constant,
Question: At 500 K, the equilibrium constant, 6Kc, for the following reaction is 5. 1/2 H2 (g) +1/2 I2 (g) ⇌ HI (g) What would be the equilibrium constant Kc for the reaction 2HI (g) ⇌ H2 (g) + I2 (g) (i) 0.04 (ii) 0.4 (iii) 25 (iv) 2.5 Solution: Option (I)0.04 is the answer....
Read More →Show that the curves
Question: Show that the curves $\frac{\mathrm{x}^{2}}{\mathrm{a}^{2}+\lambda_{1}}+\frac{\mathrm{y}^{2}}{\mathrm{~b}^{2}+\lambda_{1}}=1$ and $\frac{\mathrm{x}^{2}}{\mathrm{a}^{2}+\lambda_{2}}+\frac{\mathrm{y}^{2}}{\mathrm{~b}^{2}+\lambda_{2}}=1$ interest at right angles Solution: Given: Curves $\frac{\mathrm{x}^{2}}{\mathrm{a}^{2}+\lambda_{1}}+\frac{\mathrm{y}^{2}}{\mathrm{~b}^{2}+\lambda_{1}}=1 \ldots$ (1) $\ \frac{x^{2}}{a^{2}+\lambda_{2}}+\frac{y^{2}}{b^{2}+\lambda_{2}}=1$ First curve is $\fra...
Read More →What will be the correct order of vapour
Question: What will be the correct order of vapour pressure of water, acetone and ether at 30C. Given that among these compounds, water has a maximum boiling Do point and ether have a minimum boiling point? (i) Water ether acetone (ii) Water acetone ether (iii) Ether acetone water (iv) Acetone ether water Solution: Option (ii) Water acetone etheris the answer....
Read More →Find the slope of a line which passes through the points
Question: Find the slope of a line which passes through the points (i) $(0,0)$ and $(4,-2)$ (ii) $(0,-3)$ and $(2,1)$ (iii) $(2,5)$ and $(-4,-4)$ (iv) $(-2,3)$ and $(4,-6)$ Solution: If a line passing through $\left(x_{1}, y_{1}\right) \\left(x_{2}, y_{2}\right)$ then slope of the line is given by slope $=\left(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\right)$ (i) Given points are $(0,0)$ and $(4,-2)$ slope $=\left(\frac{-2-0}{4-0}\right)$ $=\frac{-1}{2}$ (ii) Given points are $(0,-3)$ and $(2,1)$ slope $...
Read More →On increasing the pressure,
Question: On increasing the pressure, in which direction will the gas-phase reaction proceed to re-establish equilibrium, is predicted by applying Le Chateliers principle. Consider the reaction. N2 (g) + 3H2 (g) ⇌ 2NH3 (g) Which of the following is correct, if the total pressure at which the equilibrium is established, is increased without changing the temperature? (i) K will remain the same (ii) K will decrease (iii) K will increase (iv) K will increase initially and decrease when pressure is v...
Read More →Find the condition for the following set of curves to interest orthogonally.
Question: Find the condition for the following set of curves to interest orthogonally. $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ and $\frac{x^{2}}{A^{2}}-\frac{y^{2}}{B^{2}}=1$ Solution: Given: Curves $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ ..(1) $\ \frac{x^{2}}{A^{2}}-\frac{y^{2}}{B^{2}}=1$ ....(2) First curve is $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ Differentiating above w.r.t $x$, $\Rightarrow \frac{2 x}{a^{2}}-\frac{2 y}{b^{2}} \cdot \frac{d y}{d x}=0$ $\Rightarrow \frac{y}{b^{2}...
Read More →Which of the following options
Question: Which of the following options will be correct for the stage of half completion of the reaction A ⇌ B (i) ∆Gᶱ= 0 (ii) ∆Gᶱ 0 (iii) ∆Gᶱ 0 (iv) ∆Gᶱ= RT ln2. Solution: Option(i) ∆Gᶱ= 0 is the answer....
Read More →Ka for CH3COOH is 1.8 × 10–5
Question: Ka for CH3COOH is 1.8 105 and Kb for NH4OH is 1.8 105. The pH of ammonium acetate will be (i) 7.005 (ii) 4.75 (iii) 7.0 (iv) Between 6 and 7 Solution: Option (iii)7.0is the answer....
Read More →Find the inclination of a line whose slope is
Question: Find the inclination of a line whose slope is (i) $\sqrt{3}$ (ii) $\frac{1}{\sqrt{3}}$ (iii) 1 (iv) $-1$ (v) $-\sqrt{3}$ Solution: We know that the slope of a given line is given by Slope $=\tan \theta$ Where $\theta$ angle of inclination (i) $\tan \theta=\sqrt{3}$ $\Rightarrow \theta=\tan ^{-1}(\sqrt{3})$ $\Rightarrow \theta=60^{\circ}$ (ii) $\tan \theta=\frac{1}{\sqrt{3}}$ $\Rightarrow \theta=\tan ^{-1}\left(\frac{1}{\sqrt{3}}\right)$ $\Rightarrow \theta=30^{\circ}$ (iii) $\tan \thet...
Read More →What will be the value of pH of 0.01
Question: What will be the value of pH of 0.01 mol dm3 CH3COOH (Ka = 1.74 105 )? (i) 3.4 (ii) 3.6 (iii) 3.9 (iv) 3.0 Solution: Option (i) 3.4is the answer....
Read More →In which of the following solvents
Question: In which of the following solvents is silver chloride most soluble? (i) 0.1 mol dm3 AgNO3 solution (ii) 0.1 mol dm3 HCl solution (iii) H2O (iv) Aqueous ammonia Solution: Option (iv) Aqueous ammoniais the answer....
Read More →Which of the following will produce
Question: Which of the following will produce a buffer solution when mixed in equal volumes? (i) 0.1 mol dm3 NH4OH and 0.1 mol dm3 HCl (ii) 0.05 mol dm3 NH4OH and 0.1 mol dm3 HCl (iii) 0.1 mol dm3 NH4OH and 0.05 mol dm3 HCl (iv) 0.1 mol dm3 CH4COONa and 0.1 mol dm3 NaOH Solution: Option (iii) 0.1 mol dm3 NH4OH and 0.05 mol dm3 HClis the answer....
Read More →The acidity of BF3 can be explained
Question: The acidity of BF3 can be explained based on which of the following concepts? (i) Arrhenius concept (ii) Bronsted Lowry concept (iii) Lewis concept (iv) Bronsted Lowry as well as Lewis concept. Solution: Option (iii) is the answer....
Read More →Ka, 2Ka and 3Ka is the respective
Question: Ka, 2Ka and 3Ka is the respective ionisation constants for the following reactions. H2S ⇌ H+ + HS HS ⇌ H+ + S2 H2S ⇌ 2H+ + S2 The correct relationship between Ka1 , Ka2 and Ka3 is (i) Ka3 = Ka1 Ka2 (ii) Ka3 = Ka1 + Ka2 (iii) Ka3 = Ka1 Ka2 (iv) Ka3 = Ka1 /Ka2 Solution: Option (i) is the answer....
Read More →Find the slope of a line whose inclination is
Question: Find the slope of a line whose inclination is (i) $30^{\circ}$ (ii) $120^{\circ}$ (iii) $135^{\circ}$ (iv) $90^{\circ}$ Solution: We know that the slope of a given line is given by Slope = tan Where = angle of inclination (i) Given that $\theta=30^{\circ}$ Slope $=\tan \left(30^{\circ}\right)=\frac{1}{\sqrt{3}}$ (ii) Given that $\theta=120^{\circ}$ Slope $=\tan \left(120^{\circ}\right)=\tan \left(90^{\circ}+30^{\circ}\right)=-\cot \left(30^{\circ}\right)=-\sqrt{3}$ (iii) Given that $\t...
Read More →Find the condition for the following set of curves to interest orthogonally.
Question: Find the condition for the following set of curves to interest orthogonally. $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ and $x y=c^{2}$ Solution: Given: Curves $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ .....(1) $\ x y=c^{2} \ldots(2)$ First curve is $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ Differentiating above w.r.t $x$, $\Rightarrow \frac{2 x}{a^{2}}-\frac{2 y}{b^{2}} \cdot \frac{d y}{d x}=0$ $\Rightarrow \frac{y}{b^{2}} \cdot \frac{d y}{d x}=\frac{x}{a^{2}}$ $\Rightarrow \frac...
Read More →The ionisation constant of an acid,
Question: The ionisation constant of an acid, Ka, is the measure of the strength of an acid. The Ka values of acetic acid, hypochlorous acid and formic acid are 1.74 105, 3.0 108 and 1.8 104 respectively. Which of the following orders of pH of 0.1 mol dm3 solutions of these acids are correct? (i) acetic acid hypochlorous acid formic acid (ii) hypochlorous acid acetic acid formic acid (iii) formic acid hypochlorous acid acetic acid (iv) formic acid acetic acid hypochlorous acid Solution: Option (...
Read More →In what ratio is the line segment joining the points A
Question: In what ratio is the line segment joining the points A(-4, 2) and B(8, 3) divided by the y-axis? Also, find the point of intersection. Solution: Let the point which cuts the join of A(-4, 2) and B(8, 3) in the ratio k : 1 be P(0, y) Formula: If $\mathrm{k}: 1$ is the ratio in which the join of two points are divided by another point $(x, y)$, then $\mathrm{x}=\frac{\mathrm{kx}_{2}+\mathrm{x}_{1}}{\mathrm{k}+1}$ $\mathrm{y}=\frac{\mathrm{ky}_{2}+\mathrm{y}_{1}}{\mathrm{k}+1}$ Taking for...
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