The instantaneous rate of reaction `2A+B to C +3D ` is given by

Options

A. `(dA)/(dt)`
B. `(1)/(2) (d[A])/(dt)`
C. `(d[B])/(dt)`
D. `(1)/(3)(d[D])/(dt)`

Answer

To find the instantaneous rate of the reaction \(2A + B \rightarrow C + 3D\), we can follow these steps:

### Step 1: Write the balanced chemical equation
The balanced chemical equation for the reaction is:
\[ 2A + B \rightarrow C + 3D \]

### Step 2: Understand the concept of instantaneous rate
The instantaneous rate of a reaction is defined as the change in concentration of a reactant or product per unit time. It is expressed in terms of the concentrations of the reactants and products.

### Step 3: Write the expression for the instantaneous rate
For the reaction \(2A + B \rightarrow C + 3D\), we can express the instantaneous rate using the change in concentrations of the reactants and products. The general form is:
\[ \text{Rate} = -\frac{1}{2} \frac{d[A]}{dt} = -\frac{d[B]}{dt} = \frac{d[C]}{dt} = \frac{1}{3} \frac{d[D]}{dt} \]

### Step 4: Assign signs to the changes in concentration
- For reactants (A and B), the change in concentration is negative because they are being consumed in the reaction.
- For products (C and D), the change in concentration is positive because they are being produced.

### Step 5: Write the final expression
Thus, the instantaneous rate of the reaction can be expressed as:
\[ \text{Rate} = -\frac{1}{2} \frac{d[A]}{dt} = -\frac{d[B]}{dt} = \frac{d[C]}{dt} = \frac{1}{3} \frac{d[D]}{dt} \]

### Step 6: Identify the correct terms
From the above expressions, we can identify the correct terms:
- \(-\frac{1}{2} \frac{d[A]}{dt}\)
- \(-\frac{d[B]}{dt}\)
- \(\frac{d[C]}{dt}\)
- \(\frac{1}{3} \frac{d[D]}{dt}\)

### Conclusion
The instantaneous rate of the reaction can be expressed in terms of the change in concentration of the reactants and products as shown above.

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