It is true that:

For the first order reaction $\mathrm{A}\to 2 \mathrm{B},1$ mole of reactant A gives $0.2$ moles of $B$ after $100$ minutes. The half life of the reaction is ...... min. (Round off to the nearest integer).

[Use $:\ln 2=0.69,\ln 10=2.3$

Properties of logarithms $:\ln x^y=y\ln x$

$\left.\ln \left(\frac{x}{y}\right)=\ln x-\ln y\right]$

(Round off to the nearest integer)

The reaction that occurs in a breath analyser, a device used to determine the alcohol level in a person's blood stream is

$2{ \mathrm{K}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7+8{\mathrm{H}}_2{\mathrm{SO}}_4+3{\mathrm{C}}_2{\mathrm{H}}_6\mathrm{O}\to 2{\mathrm{Cr}}_2{\left({\mathrm{SO}}_4\right)}_3+3{\mathrm{C}}_2{\mathrm{H}}_4{\mathrm{O}}_2+2{ \mathrm{K}}_2{\mathrm{SO}}_4+11{\mathrm{H}}_2\mathrm{O}$

If the rate of appearance of ${\mathrm{Cr}}_2{\left({\mathrm{SO}}_4\right)}_3$ is $2.67 \mathrm{mol}{ \min }^{-1}$ at a particular time, the rate of disappearance of ${\mathrm{C}}_2{\mathrm{H}}_6\mathrm{O}$ at the same time is mol ${\min }^{-1}.$ (Nearest integer)

The reaction rate for the reaction

${\left[{\mathrm{PtCl}}_4\right]}^{2-}+{\mathrm{H}}_2\mathrm{O}\rightleftharpoons {\left[\mathrm{Pt}\left({\mathrm{H}}_2\mathrm{O}\right){\mathrm{Cl}}_3\right]}^{-}+{\mathrm{Cl}}^{-}$

was measured as a function of concentrations of different species. It was observed that

$\frac{-\mathrm{d}\left[{\left[{\mathrm{PtCl}}_4\right]}^{2-}\right]}{\mathrm{dt}}=4.8\times {10}^{-5}\left[{\left[{\mathrm{PtCl}}_4\right]}^{2-}\right]-2.4\times {10}^{-3}\left[{\left[\mathrm{Pt}\left({\mathrm{H}}_2\mathrm{O}\right){\mathrm{Cl}}_3\right]}^{-}\right]\left[{\mathrm{Cl}}^{-}\right]$

where square brackets are used to denote molar concentrations. The equilibrium constant

${\mathrm{K}}_{\mathrm{c}}=X$(Nearest integer)

Value of $\frac{1}{X} is$ (question is modified.)