`2A+2C rarr2B`, rate of reaction `(+d(B))/(dt)` is equal to

Options

A. `-3/2(d(A))/(dt)`
B. `-(d(A))/(dt)`
C. `-1/3(d(A))/(dt)`
D. `+2(d(A))/(dt)`

Answer

To find the rate of reaction for the given equation \(2A + 2C \rightarrow 2B\), we can express the rates of change of concentrations of the reactants and products in terms of their stoichiometric coefficients. Here’s the step-by-step solution:

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

### Step 2: Define the rate of reaction
The rate of reaction can be expressed in terms of the change in concentration of the reactants and products over time. For a general reaction \(aA + bB \rightarrow cC + dD\), the rate can be defined as:
\[ \text{Rate} = -\frac{1}{a} \frac{d[A]}{dt} = -\frac{1}{b} \frac{d[B]}{dt} = \frac{1}{c} \frac{d[C]}{dt} = \frac{1}{d} \frac{d[D]}{dt} \]

### Step 3: Apply the stoichiometric coefficients
For our reaction, we can express the rate of disappearance of reactants and the rate of appearance of products as follows:
- For \(A\):
\[ -\frac{1}{2} \frac{d[A]}{dt} \]
- For \(C\):
\[ -\frac{1}{2} \frac{d[C]}{dt} \]
- For \(B\):
\[ \frac{1}{2} \frac{d[B]}{dt} \]

### Step 4: Set the rates equal
Since all these expressions represent the same rate of reaction, we can set them equal to each other:
\[ -\frac{1}{2} \frac{d[A]}{dt} = -\frac{1}{2} \frac{d[C]}{dt} = \frac{1}{2} \frac{d[B]}{dt} \]

### Step 5: Solve for the rate of formation of B
To find the rate of formation of \(B\), we can rearrange the equation:
\[ \frac{d[B]}{dt} = -\frac{d[A]}{dt} \]

### Final Expression
Thus, the rate of reaction in terms of the change in concentration of \(B\) is:
\[ \frac{d[B]}{dt} = -\frac{d[A]}{dt} \]