In a reversible reaction `2NO_(2)underset(k_(2))overset(k_(1))iffN_(2)O_(4)`, the rate of disappearance of `NO_(2)` is equal to

Options

A. `(2k_(1))/(k_(2))[NO_(2)]^(2)`
B. `2k_(1)[NO_(2)]^(2)-2k_(2)[N_(2)O_(4)]`
C. `2k_(1)[NO_(2)]^(2)-k_(2)[N_(2)O_(4)]`
D. `(2k_(1)-k_(2))[NO_(2)]`

Answer

B

Explanation

`2NO_2 underset(K_2)overset(k_1)hArr N_2O_4`,
For forward reaction rate `=-(1)/(2)(dNO_(2))/(dt)=(dN_(2)O_(4))/(dt)`
`=k_(1)[NO_(2)]^(2)`
For backward reaction
`"Rate"=-(dN_(2)O_(4))/(dt)=(1)/(2)(dNO_(2))/(dt)=k_(2)[N_(2)O_(4))`.
Rate of disappearance of `NO_(2)` = (Rate of disapperance of `NO_(2)`- Rate of appearence of `NO_(2)`)
`=2k_(1)[NO_(2)]^(2)-2k_(2)[N_(2)O_(4)]`.