A gaseous substance A undergoes first-order dissociation to give B, C, and D as shown: A ( g ) ⟶ 2 B ( g ) + C ( g ) + D ( g ) If the molar masses of A, B, C, and D are 450, 100, 50, and 200,

Question

A gaseous substance A undergoes first-order dissociation to give B, C, and D as shown:

$A_{(g)} ⟶ 2 B_{(g)} + C_{(g)} + D_{(g)}$

If the molar masses of A, B, C, and D are 450, 100, 50, and 200, respectively, and the rate constant of disappearance of A is $0.693 \times 1 0^{- 3} se c^{- 1}$ , then calculate the ratio of the rate of effusion initially and after 2000 seconds. Report your answer by multiplying the ratio by 13. (It is a closed vessel, and the temperature is constant.)

TestHub · Accepted Answer

A ( g ) ⟶ 2 B ( g ) + C ( g ) + D ( g ) 1 − − − − 1 − x 2 x x x t 1/2 ​ = 0.693 × 1 0 − 3 l n 2 ​ = 1000 sec After 2000 sec , n A ​ = 4 1 ​ ; x = 4 3 ​ M mi x ​ = 1 + 3 × 4 3 ​ 4 1 ​ × 450 + 2 3 ​ × 100 + 4 3 ​ × ( 50 + 200 ) ​ M mi x ​ = 138.46 r mix ​ r A ​ ​ = [ M A ​ M mix ​ ​ ​ ] × ( 1 + 3 × 4 3 ​ ) 1 ​ = [ ( 13 ) ( 450 ) 450 × 4 ​ ​ ] × 13 4 ​ = ( 13 ​ 2 ​ ) × 13 4 ​ = 13 ​ 2 ​ × 13 13 ​ × 13 4 ​ = 8

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