Observe the following reaction, `2A+B rarr C` The rate of formation of C is `2.2xx10^(-3)" M m in"^(-1)`. What is the value of `-(d[A])/(dt) ("in moL"^(-1)" m in "^(-1))` ?

Options

A. `2.2xx10^(-3)`
B. `1.1xx10^(-3)`
C. `4.4xx10^(-3)`
D. `5.5xx10^(-3)`

Explanation

To solve the problem, we need to analyze the reaction and the relationship between the rates of change of the reactants and products.

Given the reaction:
\[ 2A + B \rightarrow C \]

We know that the rate of formation of C is given as:
\[ \frac{d[C]}{dt} = 2.2 \times 10^{-3} \, \text{mol L}^{-1} \text{min}^{-1} \]

### Step 1: Relate the rate of formation of C to the rate of disappearance of A

From the stoichiometry of the reaction, we can establish the following relationships:
- For every 2 moles of A that react, 1 mole of C is formed.
- Therefore, the rate of disappearance of A is related to the rate of formation of C by the equation:
\[ -\frac{d[A]}{dt} = 2 \cdot \frac{d[C]}{dt} \]

### Step 2: Substitute the known rate of formation of C

Now, we can substitute the value of \(\frac{d[C]}{dt}\) into the equation:
\[ -\frac{d[A]}{dt} = 2 \cdot (2.2 \times 10^{-3}) \]

### Step 3: Calculate the rate of disappearance of A

Now, we perform the multiplication:
\[ -\frac{d[A]}{dt} = 2 \cdot 2.2 \times 10^{-3} = 4.4 \times 10^{-3} \, \text{mol L}^{-1} \text{min}^{-1} \]

### Final Answer

Thus, the value of \(-\frac{d[A]}{dt}\) is:
\[ 4.4 \times 10^{-3} \, \text{mol L}^{-1} \text{min}^{-1} \]