A reaction is catalysed by ${H^ + }$ ion. In presence of HA, rate constant is $2 \times {10^{ - 3}}\,{\min ^{ - 1}}$ and in presence of HB rate constant is $1 \times {10^{ - 3}}\;{\min ^{ - 1}}$, HA and HB both being strong acids, we may conclude that:
This question has multiple correct options
A. equilibrium constant is 2
B. HA is stronger acid HB
C. relative acidic strength of HA and HB is 2
D. HA is weaker acid than HB and relative strength is 0.5

Hint: Hint: Rate constant is the proportionality constant in the rate expression. The rate equation of a reaction when A to changes to B is $Rate = k[A]$
Here, k is the rate constant. The relationship between rate and concentration of reactants is expressed by rate equation.

Complete step by step answer:
Here, we have to choose the correct statement regarding HA and HB. Given that, in presence of HA and HB, rate constants are $2 \times {10^{ - 3}}\,{\min ^{ - 1}}$ and $1 \times {10^{ - 3}}\;{\min ^{ - 1}}$ respectively.
We can compare the acidity considering the value of rate constant. The larger the value of the rate constant, the stronger the acid is. Here, the rate constant of HA is more than rate constant HB. So, HA is stronger acid’ Hence, option B is correct.
The relative strength of two acids, HA and HB can be calculated by dividing the value of rate constant of HA by rate constant of HB. So, the relative strength is,
${\rm{Relative}}\;{\rm{acidic}}\;{\rm{strength}} = \dfrac{{2 \times {{10}^{ - 3}}\,{{\min }^{ - 1}}}}{{1 \times {{10}^{ - 3}}\,{{\min }^{ - 1}}}} = 2$
So, from the above calculation it is clear that the relative strength of acid and base is 2.

So, the correct answer is Option B,C.

Note:
strength is the extent to which acidic property is given by an acid. On diluting the solution, ionization occurs and more hydrogen ions come to solution which result in the increase of acidic strength. So, we can say that on dilution, concentration decreases but acidic strength increases.
According to the concept of Arrhenius, acid is the substance which is capable of furnishing hydrogen ions in aqueous solution and a base is the substance capable of releasing hydroxide ions in solution.