The activity of an old piece of wood is just 25% of the fresh piece of wood. If t_1/2 of C-14 is 6000 yr, the age of piece of wood is

• 6000 yr

• 3000 yr

• 9000 yr

• 12000 yr

For a first order reaction at 27$°$C, the ratio of time required for 75% completion to 25% completion of reaction is

• 3.0

• 2.303

• 4.8

• 0.477

If a plot of log₁₀ C versus t gives a straight line for a given reaction, then the reaction is

• zero order

• first order

• second order

• third order

The half-life period of a first order reaction is 1 min 40 s. Calculate its rate constant.

• 6.93 $\times {10}^{-3} {\min }^{-1}$

• 6.93 $\times {10}^{-3} {\mathrm{s}}^{-1}$

• 6.93 $\times {10}^{-3} \mathrm{s}$

• $6.93 \times {10}^3 \mathrm{s}$

According to Arrhenius equation, the rate constant (K) is related to temperature (T) as

• $\ln \frac{{\mathrm{K}}_2 }{{\mathrm{K}}_2 }= \frac{{\mathrm{E}}_{\mathrm{a}}}{\mathrm{R}}\left[\frac{1}{{\mathrm{T}}_1}-\frac{1}{{\mathrm{T}}_2}\right]$

• $\ln \frac{{\mathrm{K}}_2 }{{\mathrm{K}}_2 }= -\frac{{\mathrm{E}}_{\mathrm{a}}}{\mathrm{R}}\left[\frac{1}{{\mathrm{T}}_1}-\frac{1}{{\mathrm{T}}_2}\right]$

• $\ln \frac{{\mathrm{K}}_2 }{{\mathrm{K}}_2 }= \frac{{\mathrm{E}}_{\mathrm{a}}}{\mathrm{R}}\left[\frac{1}{{\mathrm{T}}_1}+\frac{1}{{\mathrm{T}}_2}\right]$

• $\ln \frac{{\mathrm{K}}_2 }{{\mathrm{K}}_2 }= - \frac{{\mathrm{E}}_{\mathrm{a}}}{\mathrm{R}}\left[\frac{1}{{\mathrm{T}}_1}+\frac{1}{{\mathrm{T}}_2}\right]$

If 50% of a radioactive substance dissociates in 15 min, then the time taken by substance to dissociate 99% will be

• 50 min

• 100 min

• 99 min

• 150 min

A certain nuclide has a half-life period of 30 min. If a sample containing 600 atoms is allowed to decay for 90 min, how many atoms will remain ?

• 200 atoms

• 450 atoms

• 75 atoms

• 150 atoms

68.

For the reaction: ${\mathrm{H}}_2 + {\mathrm{I}}_2 \to 2\mathrm{HI},$ the differential rate law is

• $-\frac{\mathrm{d} \left[{\mathrm{H}}_2\right]}{\mathrm{dt}}=-\frac{\mathrm{d} \left[{\mathrm{I}}_2\right]}{\mathrm{dt}}=2\frac{\mathrm{d}\left[\mathrm{HI}\right]}{\mathrm{dt}}$

• $-\frac{\mathrm{d} \left[{\mathrm{H}}_2\right]}{\mathrm{dt}}=-2\frac{\mathrm{d} \left[{\mathrm{I}}_2\right]}{\mathrm{dt}}=\frac{\mathrm{d}\left[\mathrm{HI}\right]}{\mathrm{dt}}$

• $-\frac{\mathrm{d} \left[{\mathrm{H}}_2\right]}{\mathrm{dt}}=-\frac{\mathrm{d} \left[{\mathrm{I}}_2\right]}{\mathrm{dt}}=\frac{\mathrm{d}\left[\mathrm{HI}\right]}{\mathrm{dt}}$

• $-\frac{\mathrm{d} \left[{\mathrm{H}}_2\right]}{\mathrm{dt}}=\frac{\mathrm{d} \left[{\mathrm{I}}_2\right]}{\mathrm{dt}}=\frac{\mathrm{d}\left[\mathrm{HI}\right]}{\mathrm{dt}}$

Which is a correct integrated rate equation?

• $\mathrm{k} = -\frac{2.303}{\mathrm{t}} \log \frac{\mathrm{a}}{\mathrm{a} - \mathrm{x}}$

• $\mathrm{k} = \frac{-2.303}{\mathrm{t}} \log \frac{\mathrm{a} - \mathrm{x}}{\mathrm{a}}$

• - d (a - x) = kdt

• All are integrated rate equations

For which order reaction, the unit of rate constant is time^-1?

• Zero order

• First order

• Second order

• Third order