For a chemical reaction starting with some initial concentration of reactant At as a function of time (t) is given by the equation, 1/("A"_"t"^4) = 2 + 1.5 xx 10^-3 t The rate of disappearance of [A] - Chemistry (JEE Main)

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For a chemical reaction starting with some initial concentration of reactant At as a function of time (t) is given by the equation,

`1/("A"_"t"^4) = 2 + 1.5 xx 10^-3` t

The rate of disappearance of [A] is ____ × 10-2 M/sec when [A] = 2 M.

[Given: [At] in M and t in sec.]
[Express your answer in terms of 10-2 M /s]
[Round off your answer if required]

Options

  • 1.3

  • 1.2

  • 5.3

  • 0.5

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Solution

The rate of disappearance of [A] is 1.2 × 10-2 M/sec when [A] = 2 M.

Explanation:

`1/("A"_"t"^4) = 2 + 1.5 xx 10^-3` t

`therefore (-4)/(["A"]_"t"^5) ("d"["A"])/"dt" = 1.5 xx 10^-3`

`therefore - ("d"["A"])/"dt" = (1.5 xx ["A"]_"t"^5 xx 10^-3)/4`

= 1.5 × 8 × 10-3

= 1.2 × 10-2 m/s

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