For the reaction 2A + B `to` C, rate of disappearance of A 0.076 `mols^-1.`
What is the rate of the overall reaction?

Answer

To find the rate of the overall reaction for the equation:

\[ 2A + B \rightarrow C \]

we start with the information given about the rate of disappearance of A, which is \( 0.076 \, \text{mol s}^{-1} \).

### Step-by-Step Solution:

1. **Identify the Stoichiometry of the Reaction**:
The balanced equation shows that 2 moles of A are consumed for every 1 mole of B and 1 mole of C produced. This means that the rate of the reaction can be expressed in terms of the change in concentration of A, B, and C.

2. **Write the Rate Expressions**:
The rate of the reaction can be expressed in terms of the change in concentration of A:
\[ \text{Rate} = -\frac{1}{2} \frac{d[A]}{dt} = -\frac{d[B]}{dt} = \frac{d[C]}{dt} \]
Here, \(-\frac{d[A]}{dt}\) is the rate of disappearance of A, and since 2 moles of A are consumed, we have a factor of \(\frac{1}{2}\).

3. **Substitute the Given Rate**:
We know that the rate of disappearance of A is given as:
\[ -\frac{d[A]}{dt} = 0.076 \, \text{mol s}^{-1} \]
Therefore, we can substitute this value into our rate expression:
\[ \text{Rate} = -\frac{1}{2} \left(0.076\right) \]

4. **Calculate the Overall Rate**:
Now, we can calculate the overall rate:
\[ \text{Rate} = -\frac{1}{2} \times 0.076 = -0.038 \, \text{mol s}^{-1} \]
Since we are interested in the overall rate (which is positive), we take the absolute value:
\[ \text{Overall Rate} = 0.038 \, \text{mol s}^{-1} \]

### Final Answer:
The rate of the overall reaction is \( 0.038 \, \text{mol s}^{-1} \).