`2N_(2)O_(5) rarr 4NO_(2) + O_(2)`
If `(-d[N_(2)O_(5)])/(dt) = k_(1)[N_(2)O_(5)]`
`(d[NO_(2)])/(dt) = k_(2)[N_(2)O_(5)]`
`(d[O_(2)])/(dt) = k_(3)[N_(2)O_(5)]`
What is the relation between `k_(1), k_(2)`, and `k_(3)`?

Options

A. `k' = 2k, k' = k`
B. `k' = 2k, k'' = k`
C. `k' = 2k, k'' = 2k`
D. `k' = k, k'' = k`

Answer

B

Explanation

Rate of disappearance of reactants `=` Rate of apperance of products
`-(1)/(2)(d[N_(2)O_(5)])/(d t) = (1)/(4)(d[NO_(2)])/(d t) = (d(O_(2)))/(d t)`
`(1)/(2)k(N_(2)O_(5)) = (1)/(4)k' (N_(2)O_(5)) = k''(N_(2)O_(5))`
`(k)/(2) = (k')/(4) = k'' " "k = 2k, k'' = (k)/(2)`