Chapter 12 Multiple choice questions

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. Consider the Bragg equation nλ = 2d sin θ. Which of the answers a-d below is the correct result of rearranging the equation to make θ the subject?

$\theta ={\sin }^{-1}\left(\frac{2d}{n\lambda }\right)$ correct incorrect

$\theta ={\sin }^{-1}\left(\frac{n\lambda }{2d}\right)$ correct incorrect

$\theta =\frac{{\sin }^{-1}\left(2d\right)}{n\lambda }$ correct incorrect

$\theta =\raisebox{1ex}{$\left(\frac{n\lambda }{2d}\right)$}\!\left/ \!\raisebox{-1ex}{$\sin $}\right.$ correct incorrect

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. Consider the Debye-Hückel equation: $\log \gamma =-Az+z-\sqrt{I}$.
Which of the answers a-d below is the correct result of rearranging the equation to make ionic strength I the subject?

$I\text{}=\frac{{\left(\log \gamma \right)}^2}{A{z}_{+}{z}_{-}}$ correct incorrect

$I\text{}={\left(A{z}_{+}{z}_{-}+\log \gamma \right)}^2$ correct incorrect

$I\text{}=\sqrt{\frac{\log \gamma }{A{z}_{+}{z}_{-}}}$ correct incorrect

$I\text{}={\left(\frac{\log \gamma }{A{z}_{+}{z}_{-}}\right)}^2$ correct incorrect

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. Consider the Nernst equation, $E=E^{⦵}+\frac{RT}{nF}\ln \left(\frac{\left[\mathrm{O}\right]}{\left[\mathrm{R}\right]}\right)$.
Which of the answers a-d below is the correct result of rearranging the equation to make concentration [O] the subject?

$\text{[O]=[R]}\exp \left(\frac{nF\left(E-E^{\sout{0}}\right)}{RT}\right)$ correct incorrect

$\text{[O]=[R]}\exp \left(\left(E-E^{\sout{0}}\right)-\frac{RT}{nF}\right)$ correct incorrect

$\text{[O]=}\exp \left(\frac{nF\left(E-E^{\sout{o}}\right)}{RT}\right)-\text{[R]}$ correct incorrect

$\text{[O]=}\exp \left(\frac{nF\left(E-E^{\sout{o}}\right)}{RT}\right)+\text{[R]}$ correct incorrect

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. Consider the van't Hoff isotherm, ∆G = -RT ln K. Which of the answers a-d below is the correct result of rearranging the equation to make K the subject?

$\exp (∆\mathrm{G}+\mathrm{RT})$ correct incorrect

$\exp \left[-\frac{∆\mathrm{G}}{\mathrm{RT}}\right]$ correct incorrect

$-\exp \left[\frac{∆\mathrm{G}}{\mathrm{RT}}\right]$ correct incorrect

$\frac{\exp (∆G)}{-RT}$ correct incorrect

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. Rearrange the expression pH = -log [H⁺] to make the concentration term the subject. Which of the following is the correct answer?

exp(-pH) correct incorrect

10^pH correct incorrect

10^-pH correct incorrect

exp(pH) correct incorrect

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. Consider the Clausius-Clapeyron equation, $\ln \left(\frac{p_2}{p_1}\right)=-\frac{\Delta H}{R}\left(\frac{1}{T_2}-\frac{1}{T_2}\right)$.
Which of the answers a-d below is the correct result of rearranging the equation to make p₂ the subject?

$p_2=p_1\exp \left(-\frac{\Delta H}{R}\left(\frac{1}{T_2}-\frac{1}{T_2}\right)\right)$ correct incorrect

$p_2=-p_1\exp \left(\frac{\Delta H}{R}\left(\frac{1}{T_2}-\frac{1}{T_2}\right)\right)$ correct incorrect

$p_2=\exp \left(\frac{\Delta H}{R}\left(\frac{1}{T_2}-\frac{1}{T_2}\right)\right)-p_1$ correct incorrect

$p_2=\exp \left(\frac{\Delta H}{R}\left(\frac{1}{T_2}-\frac{1}{T_2}\right)\right)/p_1$ correct incorrect

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. The volume V of a code of height h and radius r is, $\frac{\pi r^{2}h}{3}$
Which of the answers a-d below is the correct result of rearranging the equation to make the radius r the subject?

$r=\frac{3V}{\pi h}$ correct incorrect

$r=\sqrt{\frac{\pi h}{3V}}$ correct incorrect

$r=\frac{\pi h}{3V}$ correct incorrect

$r=\sqrt{\frac{3V}{\pi h}}$ correct incorrect

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. The Schulze-Hardy rule relates the critical coagulation concentration (CCC) of a colloid, the valence of extra counterionic electrolytes (z), with a simple mathematical relationship of [CCC] = k/z⁶.
Which of the answers a-d below is the correct result of rearranging the equation to make the charge z the subject?

$z=\frac{k}{\text{6[CCC]}}$ correct incorrect

$z=\sqrt[6]{\frac{k}{\text{[CCC]}}}$ correct incorrect

$z=\sqrt[]{\frac{k}{\text{[CCC]}}}$ correct incorrect

$z=\frac{k}{\text{[CCC]}}$ correct incorrect

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. Two atoms connected by a chemical bond often act much like a spring. The bond force constant k, the reduced mass μ, and the frequency of oscillation ω are connected k = μω².
Which of the answers a-d below is the correct result of rearranging the equation to make the frequency ω the subject?

$\omega =\sqrt{\frac{k}{\mu }}$ correct incorrect

$\omega =\sqrt{k-\mu }$ correct incorrect

$\omega =\sqrt{k\mu }$ correct incorrect

$\omega ={\left(\frac{k}{\mu }\right)}^2$ correct incorrect

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. Consider a right-angled triangle. The length of the hypotenuse is h. The length of the adjacent a is given as a = h sin θ.
Which of the answers a-d below is the correct result of rearranging the equation to make the angle θ?

$\theta ={\sin }^{-1}\left(a-h\right)$ correct incorrect

$\theta ={\sin }^{-1}\left(a+h\right)$ correct incorrect

$\theta ={\sin }^{-1}\left(\frac{h}{a}\right)$ correct incorrect

$\theta ={\sin }^{-1}\left(\frac{h}{a}\right)$ correct incorrect