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Question: The differential rate law for the reaction H2 + I2® 2HI is :...

The differential rate law for the reaction H2 + I2® 2HI is :

A

−d[H2]dt=−d[l2]dt=−d[Hl]dt- \frac{d\left\lbrack H_{2} \right\rbrack}{dt} = - \frac{d\left\lbrack l_{2} \right\rbrack}{dt} = - \frac{d\lbrack Hl\rbrack}{dt}

B

d[H2]dt=d[l2]dt=12d[Hl]dt\frac{d\left\lbrack H_{2} \right\rbrack}{dt} = \frac{d\left\lbrack l_{2} \right\rbrack}{dt} = \frac{1}{2}\frac{d\lbrack Hl\rbrack}{dt}

C

12d[H2]dt=12d[l2]dt=−d[Hl]dt\frac{1}{2}\frac{d\left\lbrack H_{2} \right\rbrack}{dt} = \frac{1}{2}\frac{d\left\lbrack l_{2} \right\rbrack}{dt} = - \frac{d\lbrack Hl\rbrack}{dt}

D

−2d[H2]dt=−2d[l2]dt=+d[Hl]dt- 2\frac{d\left\lbrack H_{2} \right\rbrack}{dt} = - 2\frac{d\left\lbrack l_{2} \right\rbrack}{dt} = + \frac{d\lbrack Hl\rbrack}{dt}

Answer

−2d[H2]dt=−2d[l2]dt=+d[Hl]dt- 2\frac{d\left\lbrack H_{2} \right\rbrack}{dt} = - 2\frac{d\left\lbrack l_{2} \right\rbrack}{dt} = + \frac{d\lbrack Hl\rbrack}{dt}

Explanation

Solution

H2 + □2 ® 2H□

When 1 mole of H2 and 1mole of I2 reacts, 2 moles of HI are formed in the same time interval.

Thus the rate may be expressed as

−Δ[H2]Δt=Δ[l2]Δt=12Δ[Hl]Δt\frac{- \Delta\left\lbrack H_{2} \right\rbrack}{\Delta t} = \frac{\Delta\left\lbrack l_{2} \right\rbrack}{\Delta t} = \frac{1}{2}\frac{\Delta\lbrack Hl\rbrack}{\Delta t}The negative sign signifies a decrease in concentration of the reactant with increase of time.