For a reaction \(A\text{ + }B \longrightarrow C\text{ + }D\) if the concentration of A is doubled without altering the concentration of B, the rate gets doubled. If the concentration of B is increased by nine times without altering the concentration of A, the rate gets tripled. The order of the reaction is:
Answer & explanation
Correct answer: option 3
The correct answer is option 3. \(\frac{3}{2}\).
The given reaction is
\(A\text{ + }B \longrightarrow C\text{ + }D\)
So,
\(r = k [A]^{\alpha} [B]^{\beta}\) -------(1)
\(2r = k [2A]^{\alpha} [B]^{\beta}\) -------(2)
\(3r = k [A]^{\alpha} [9B]^{\beta}\) -------(3)
Dividing equation (3) by (1),we get
\(3 = 9^{\beta}\)
or, \(3^1 = 3^{2 \beta}\)
or, \(2 \beta = 1\)
or, \(\beta = \frac{1}{2}\)
Dividing equation (2) by (1),we get
\(2 = 2^{\alpha }\)
or, \(2^1 = 2^{\alpha }\)
or, \(\alpha = 1\)
So, the order of the reaction will be
\(\alpha + \beta = 1 + \frac{1}{2} = \frac{3}{2}\)