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Chemistry-

General

Easy

Question

For the reaction $A plus B rightwards arrow C plus D$ , doubling the concentration of both the reactants increases the reaction rate by 8 times and doubling the initial concentration of only B simply doubles the reaction rate. The rate law for the reaction is

(a) $r = k [A] {[B]}^{2}$
(b) $r = k [A] [B]$
(c) $r = k {[A]}^{1 / 2} [B]$
(d) $r = k {[A]}^{2} [B]$

The correct answer is: (d) $r equals k open square brackets A close square brackets to the power of 2 end exponent left square bracket B right square bracket$

For the reaction $A plus B ⟶ C plus D$
Rate of reaction:
$r subscript 1 end subscript equals k open square brackets A close square brackets to the power of x end exponent open square brackets B close square brackets to the power of y end exponent$ …(i)
$r subscript 2 end subscript equals 8 r subscript 1 end subscript equals k open square brackets 2 A close square brackets to the power of x end exponent open square brackets 2 B close square brackets to the power of y end exponent$ …(ii)
$r subscript 3 end subscript equals 2 r subscript 1 end subscript equals k open square brackets A close square brackets to the power of x end exponent open square brackets 2 B close square brackets to the power of y end exponent$ …(iii)
Dividing equation (iii) by (i),
$fraction numerator 2 r subscript 1 end subscript over denominator r subscript 1 end subscript end fraction equals fraction numerator k open square brackets A close square brackets to the power of x end exponent open square brackets 2 B close square brackets to the power of y end exponent over denominator k open square brackets A close square brackets to the power of x end exponent open square brackets B close square brackets to the power of y end exponent end fraction$
$open parentheses 2 close parentheses to the power of 1 end exponent equals open parentheses 2 close parentheses to the power of y end exponent$
$y equals 1$
Dividing equation (ii) by (i),
$fraction numerator 8 r subscript 1 end subscript over denominator r subscript 2 end subscript end fraction equals fraction numerator k open square brackets 2 A close square brackets to the power of x end exponent open square brackets 2 B close square brackets to the power of y end exponent over denominator k open square brackets A close square brackets to the power of x end exponent open square brackets B close square brackets to the power of y end exponent end fraction$
$8 equals open parentheses 2 x close parentheses to the power of x end exponent open parentheses 2 close parentheses to the power of y end exponent$
$8 equals open parentheses 2 close parentheses to the power of x end exponent open parentheses 2 close parentheses to the power of 1 end exponent$
$4 equals open parentheses 2 close parentheses to the power of x end exponent$
$open parentheses 2 close parentheses to the power of 2 end exponent equals open parentheses 2 close parentheses to the power of x end exponent$
$x equals 2$
$therefore r equals k open square brackets A close square brackets to the power of 2 end exponent left square bracket B right square bracket$

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