For the reaction : `A + 2B rarr C + D`, the expression of rate of reaction will be :

Options

A. `(-1)/(1) (d[A])/(dt) = (-1)/(2)(d[B])/(dt)`
B. `1/1(d[A])/(dt) = (-1)/(2) (d[B])/(dt)`
C. `(-1)/(1) (d[A])/(dt) = 1/2(d[B])/(dt)`
D. `1/1(d[A])/(dt) =(-1)/(2) (d[B])/(dt)`

Answer

To determine the expression for the rate of the reaction given by the equation:

\[ A + 2B \rightarrow C + D \]

we can follow these steps:

### Step 1: Write the Rate of Reaction
The rate of a reaction is generally expressed in terms of the change in concentration of reactants and products over time. For the reaction given, we can express the rate in terms of the reactants and products as follows:

\[ \text{Rate} = -\frac{1}{1} \frac{d[A]}{dt} = -\frac{1}{2} \frac{d[B]}{dt} = \frac{1}{1} \frac{d[C]}{dt} = \frac{1}{1} \frac{d[D]}{dt} \]

### Step 2: Assign Coefficients
In the reaction \( A + 2B \rightarrow C + D \), the coefficients of the reactants and products are important for the rate expression. Here, the coefficient of \( A \) is 1, the coefficient of \( B \) is 2, and the coefficients of \( C \) and \( D \) are both 1.

### Step 3: Formulate the Rate Expression
From the stoichiometry of the reaction, we can formulate the rate expression. The rate of reaction can be expressed as:

\[ \text{Rate} = k [A]^1 [B]^2 \]

where \( k \) is the rate constant.

### Step 4: Combine the Expressions
Now, we can combine the expressions for the rate of change of concentration of reactants and products. The overall expression becomes:

\[ \text{Rate} = -\frac{d[A]}{dt} = -\frac{1}{2} \frac{d[B]}{dt} = \frac{d[C]}{dt} = \frac{d[D]}{dt} \]

### Final Expression
Thus, the final expression for the rate of the reaction can be summarized as:

\[ \text{Rate} = k [A]^1 [B]^2 \]