For a chemical reaction, `m_1A+m_2B rarrn_1C+n_2D` The ratio of rate of disappearance of A to that of appearance of C is

Options

A. `m_1//m_2`
B. `m_2//m_1`
C. `n_1//m_1`
D. `m_1//n_1`

Answer

To solve the problem of finding the ratio of the rate of disappearance of A to that of the appearance of C in the reaction \( m_1A + m_2B \rightarrow n_1C + n_2D \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Rate of Reaction**:
The rate of a reaction is defined as the change in concentration of a reactant or product over time. For reactants, the rate is negative because they are consumed, while for products, the rate is positive because they are formed.

2. **Write the Rate Expressions**:
For the reactant A, the rate of disappearance can be expressed as:
\[ \text{Rate of disappearance of A} = -\frac{1}{m_1} \frac{d[A]}{dt} \]
For the product C, the rate of appearance can be expressed as:
\[ \text{Rate of appearance of C} = \frac{1}{n_1} \frac{d[C]}{dt} \]

3. **Set Up the Ratio**:
We need to find the ratio of the rate of disappearance of A to the rate of appearance of C:
\[ \text{Ratio} = \frac{\text{Rate of disappearance of A}}{\text{Rate of appearance of C}} = \frac{-\frac{1}{m_1} \frac{d[A]}{dt}}{\frac{1}{n_1} \frac{d[C]}{dt}} \]

4. **Simplify the Ratio**:
By rearranging the terms, we can simplify the ratio:
\[ \text{Ratio} = \frac{-\frac{1}{m_1} \frac{d[A]}{dt}}{\frac{1}{n_1} \frac{d[C]}{dt}} = -\frac{n_1}{m_1} \cdot \frac{\frac{d[A]}{dt}}{\frac{d[C]}{dt}} \]
Since we are interested in the absolute values, we can ignore the negative sign:
\[ \text{Ratio} = \frac{n_1}{m_1} \]

5. **Final Answer**:
Thus, the ratio of the rate of disappearance of A to that of the appearance of C is:
\[ \frac{n_1}{m_1} \]