The rate of a reaction depends upon the

Options

A. Volume
B. Force
C. Pressure
D. Concentration of reactant

Answer

To solve the question regarding the rate of a reaction, we need to establish the differential rate law based on the given reaction. Here’s a step-by-step breakdown of how to derive the rate equation:

### Step 1: Identify the Reaction
The reaction provided is:
\[ 3A + B \rightarrow C + D \]

### Step 2: Write the Rate of Reaction
The rate of a reaction can be expressed in terms of the change in concentration of the reactants and products over time. For the given reaction, we can express the rate as:
\[ \text{Rate} = -\frac{1}{3} \frac{d[A]}{dt} = -\frac{d[B]}{dt} = \frac{d[C]}{dt} = \frac{d[D]}{dt} \]

### Step 3: Understand the Signs
- The negative sign indicates that the concentration of reactants (A and B) decreases as the reaction proceeds.
- The positive sign indicates that the concentration of products (C and D) increases as the reaction proceeds.

### Step 4: Write the Differential Rate Law
From the above expressions, we can summarize the differential rate law as:
\[ -\frac{1}{3} \frac{d[A]}{dt} = -\frac{d[B]}{dt} = \frac{d[C]}{dt} = \frac{d[D]}{dt} \]

### Step 5: Match with Options
Now, we can match this derived equation with the options provided in the question to find the correct one. The first option matches our derived equation.

### Final Answer
Thus, the rate of the reaction can be represented by:
\[ -\frac{1}{3} \frac{d[A]}{dt} = -\frac{d[B]}{dt} = \frac{d[C]}{dt} = \frac{d[D]}{dt} \]

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