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Solubility Product

In a certain ...

Question

In a certain gaseous reaction between A and B, A + 3B $\to A B_{3} .$ The initial rates are reported as follows: The rate law is $r = k [A]^{x} [B]^{y}$ ,
value of x+y is :
[A] [B] Rate
0.1 M 0.1 M 0.002 M $s^{- 1}$
0.2 M 0.1 M 0.002 M $s^{- 1}$
0.3 M 0.2 M 0.008 M $s^{- 1}$
0.4 M 0.3 M 0.018 M $s^{- 1}$

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Solution

In experiments I and II, [B] is constant and [A] is doubled. The rate does not change. So order w.r.t. [A] = Zero.
Let rate = $k [A]^{0} [B]^{x}$
$r_{2} = 0.002 M s^{- 1} = k [0.1]^{x}$
$r_{2} = 0.008 M s^{- 1} = k [0.2]^{x}$
$\frac{r_{3}}{r_{2}} = 4 = (2)^{x}$
$∴ (2)^{2} = (2)^{x}$
X = 2
So order w.r.t. [B] = 2
Rate = $k [A]^{0} [B]^{2}$

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Q. In a certain gaseous reaction between A and B, A + 3B

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[A]	[B]	Rate
0.1 M	0.1 M	0.002 M $s^{- 1}$
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