\(A _{( g )}+2 B _{( g )} \rightarrow C _{( g )}\) In the reaction represented by the equation above, the rate of appearance of \(C\) is found experimentally to be independent of the concentration of A and to increase four folds when the concentration of B is doubled. The rate law for the reaction is ____________
A. Rate \(=K[A]^{0}[B]^{4}\) B. Rate \(= K [A]^{0}[B]^{2}\) C. Rate \(= K [A][B]^{2}\) D. Rate \(= K [A]^{2}[B]^{0}\)
Correct Answer: B
Explanation
Let the rate of the appearance of \(C\) be \(r\). Then \(r \alpha[ A ]^{\circ}\) (i.e. \(r\) is independent of the concentration of \(A\) ) \(r \alpha[B]^{2}\) (i.e. \(r\) increases four \(-\) fold when \([B]\) is doubled) Hence, rate, \(r \alpha[A]^{0}[B]^{2}\), \(r=k[A]^{\circ}[B]^{2}\)
