JEE Advanced2021ChemistryChemical KineticsActual
For the following reaction 2 X + Y → k P the rate of reaction is d [ P ] dt = k [ X ] . Two moles of X are mixed with one mole of Y to make 1 . 0   L of solution. At 50   s ,   0 . 5 mole of Y is left in the reaction mixture. The correct statement(s) about the reaction is(are) ( Use: ln   2 = 0 . 693 )
Options
- AThe rate constant, k , of the reaction is 13 . 86 × 10 - 4   s - 1 .
- BHalf-life of X is 50   s .
- CAt 50   s ,   - d [ x ] dt = 13 . 86 × 10 - 3   mol   L - 1   s - 1 .
- DAt 100   s , - d Y dt = 3 . 46 × 10 - 3   mol   L - 1   s - 1
Correct answer
B. Half-life of X is 50   s .
Step-by-step solution
( array lllll & 2 X + & y & & P t =0 & 2 & 1 & & 0 t =50 & 2-2 0.5 & 1-0.5 & & & 1mole & 0.5 & & array ) rate (=- 1 2 d x d t =- d y d t = d P d t =K[X] ) (- 1 2 d x d t =K[X] ) (- d x d t =2 K[X]=K^1[X] ) Half life is (t=50 sec ) (2 K= 0.653 L 50 ) (K= 0.6932 100 =6.332 10⁻³ ) (t=50 sec ) (- d x d t =2 K[X] ) (- d x d t =2 6.332 10⁻³ 1 ) (=13.864 10⁻³ ~mole / L / Sec ) (- d y d t =K[X]=6.332 10⁻³ ( 1 2 ) ) (=3.46 10⁻³ ~mole / L / Sec ⁻¹ )