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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

For the reaction A + B → P. If [B] is doubled at constant [A], the rate of reaction doubled. If [A] is triple and [B] is doubled, the rate of reaction increases by a factor of 6. Calculate the rate

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प्रश्न

For the reaction A + B → P.

If [B] is doubled at constant [A], the rate of reaction doubled. If [A] is triple and [B] is doubled, the rate of reaction increases by a factor of 6. Calculate the rate law equation.

संख्यात्मक
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उत्तर

Given: A + B → P

∴ Rate of reaction,

rate = k[A]x [B]y    ...(i)

If [B] is doubled at constant [A], the rate of reaction doubled.

∴ 2 × rate = k[A]x [2B]y

∴ 2 × rate = k[A]x 2y [2B]y    ...(ii)

If [A] is tripled and [B] is doubled, the rate of reaction increases by a factor of 6.

∴ 6 × rate = k[3A]x [2B]y   

6 × rate = 3x k[3A]x 2y [B]y     ...(iii)

Divide equation (ii) by (i), we get

`(2 xx "rate")/"rate" = (k[A]^x  2^y[B]^y)/(k[A]^x  [B]^y)`

21 = 2y

∴ y = 1

Now divide equation (iii) by (i), we get

`(6 xx "rate")/"rate" = (3^x  k[A]^x  2^y [B]^y)/(k[A]^x  [B]^y)`

6 = 3x2y

= 3x × 2    ...(∵ y = 1)

∴ x = 1

Now, x = 1 and y = 1 values should be written in the equation (i)

∴ The rate law can be written as

rate = k[A]1 [B]1

rate = k[A][B]

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