For a reaction of type
`aA+bBrarr"products", (-d[A])/(dt)` is equal to

Options

A. `(-d[B])/(dt)`
B. `-b/d(d[B])/(dt)`
C. `-a/(b)xx(d[B])/(dt)`
D. `-b/(a)xx(d[B])/(dt)`

Answer

To solve the question regarding the reaction of type \( aA + bB \rightarrow \text{products} \) and to express \(-\frac{d[A]}{dt}\) in terms of the stoichiometric coefficients, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Reaction**:
The reaction is given as \( aA + bB \rightarrow \text{products} \). Here, \( A \) and \( B \) are the reactants, and \( a \) and \( b \) are their respective stoichiometric coefficients.

2. **Rate of Reaction**:
The rate of reaction can be expressed in terms of the change in concentration of the reactants over time. For reactant \( A \), the rate of disappearance is given by:
\[ -\frac{d[A]}{dt} \]
For reactant \( B \), the rate of disappearance is:
\[ -\frac{d[B]}{dt} \]

3. **Relating Rates to Stoichiometry**:
The relationship between the rates of disappearance of the reactants and the formation of products can be expressed using their stoichiometric coefficients:
\[ -\frac{1}{a} \frac{d[A]}{dt} = -\frac{1}{b} \frac{d[B]}{dt} \]
This means that the rate of disappearance of \( A \) is proportional to its stoichiometric coefficient \( a \), and similarly for \( B \) with coefficient \( b \).

4. **Expressing \(-\frac{d[A]}{dt}\)**:
Rearranging the above equation gives:
\[ -\frac{d[A]}{dt} = \frac{a}{b} \left(-\frac{d[B]}{dt}\right) \]
This indicates that the rate of disappearance of \( A \) can be expressed in terms of the rate of disappearance of \( B \) and their stoichiometric coefficients.

5. **Final Expression**:
Thus, the expression for \(-\frac{d[A]}{dt}\) in terms of the concentration change of \( B \) is:
\[ -\frac{d[A]}{dt} = \frac{a}{b} \left(-\frac{d[B]}{dt}\right) \]