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If the half-life $(t_{1/2})$ for a first order reaction is 1 minute, then the time required for 99.9% completion of the reaction is closest to:
99.9% completion leaves $1/1000$ remaining. $\left(\tfrac12\right)^n = \tfrac{1}{1000}\Rightarrow n\approx10$ half-lives $= 10$ minutes.
The correct order of the wavelength of light absorbed by the following complexes is: A. $[\text{Co(NH}_3)_6]^{3+}$, B. $[\text{Co(CN)}_6]^{3-}$, C. $[\text{Cu(H}_2\text{O)}_4]^{2+}$, D. $[\text{Ti(H}_2\text{O)}_6]^{3+}$. Choose the correct answer:
Larger crystal-field splitting $\Delta$ means shorter absorbed wavelength. $\Delta$: B (CN⁻) > A (NH₃) > D (Ti³⁺/H₂O) > C (Cu²⁺/H₂O). So wavelength increases as B < A < D < C.
Which one of the following compounds can exist as cis-trans isomers?
1,2-Dimethylcyclohexane has two different groups on each of two ring carbons → cis and trans isomers exist. The others lack the required geometric restriction.
Phosphoric acid ionizes in three steps with their ionization constant values $K_{a_1}$, $K_{a_2}$ and $K_{a_3}$, respectively, while K is the overall ionization constant. Which of the following statements are true? A. $\log K = \log K_{a_1} + \log K_{a_2} + \log K_{a_3}$. B. $\text{H}_3\text{PO}_4$ is a stronger acid than $\text{H}_2\text{PO}_4^-$ and $\text{HPO}_4^{2-}$. C. $K_{a_1} > K_{a_2} > K_{a_3}$. D. $K_{a_1} = \dfrac{K_{a_3}+K_{a_2}}{2}$. Choose the correct answer:
$K = K_{a_1}K_{a_2}K_{a_3}\Rightarrow\log K = \sum\log K_{a_i}$ (A true). Successive ionization weakens: $K_{a_1} > K_{a_2} > K_{a_3}$ (C true) and $\text{H}_3\text{PO}_4$ is the strongest (B true). D is false.
Which one of the following reactions does NOT give benzene as the product?
Benzene diazonium chloride with warm water gives phenol (and N₂), not benzene. The other three (decarboxylation, aromatization of hexane, cyclic trimerization of ethyne) all give benzene.
If the molar conductivity $(\Lambda_m)$ of a $0.050\ \text{mol L}^{-1}$ solution of a monobasic weak acid is $90\ \text{S cm}^2\text{mol}^{-1}$, its extent (degree) of dissociation will be [Assume $\Lambda^\circ_+ = 349.6\ \text{S cm}^2\text{mol}^{-1}$ and $\Lambda^\circ_- = 50.4\ \text{S cm}^2\text{mol}^{-1}$]:
$\Lambda^\circ_m = 349.6 + 50.4 = 400$. $\alpha = \dfrac{\Lambda_m}{\Lambda^\circ_m} = \dfrac{90}{400} = 0.225$.
Given below are two statements:
Statement I: A hypothetical diatomic molecule with bond order zero is quite stable.
Statement II: As bond order increases, the bond length increases.
In the light of the above statements, choose the most appropriate answer:
Bond order zero means the molecule does not exist / is unstable (I false). Bond length decreases (not increases) with increasing bond order (II false).
Out of the following complex compounds, which of the compound will be having the minimum conductance in solution?
$[\text{Co(NH}_3)_3\text{Cl}_3]$ is a non-electrolyte (no ions in solution), so it has the minimum conductance.
Match List-I with List-II:
List-I — A. $\text{XeO}_3$, B. $\text{XeF}_2$, C. $\text{XeOF}_4$, D. $\text{XeF}_6$
List-II — I. $sp^3d$; linear, II. $sp^3$; pyramidal, III. $sp^3d^3$; distorted octahedral, IV. $sp^3d^2$; square pyramidal
Choose the correct answer:
$\text{XeO}_3$: $sp^3$ pyramidal (II); $\text{XeF}_2$: $sp^3d$ linear (I); $\text{XeOF}_4$: $sp^3d^2$ square pyramidal (IV); $\text{XeF}_6$: $sp^3d^3$ distorted octahedral (III).
$\text{C(s)} + 2\text{H}_2\text{(g)} \to \text{CH}_4\text{(g)}$; $\Delta H = -74.8\ \text{kJ mol}^{-1}$. Which of the following diagrams gives an accurate representation of the above reaction? [R → reactants; P → products]
$\Delta H$ is negative (exothermic), so the products lie below the reactants by 74.8 kJ mol⁻¹, with an activation hump in between.
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