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 problem, we need to express the rate of change of concentration of reactant A in terms of the rate of change of concentration of reactant B. The reaction is given as:

\[ aA + bB \rightarrow \text{products} \]

### Step-by-Step Solution:

1. **Write the Rate Expression**:
The rate of the reaction can be expressed in terms of the change in concentration of A and B. The rate of disappearance of A can be written as:
\[ -\frac{d[A]}{dt} = \frac{1}{a} \frac{d[A]}{dt} \]
Similarly, for B, it can be expressed as:
\[ -\frac{d[B]}{dt} = \frac{1}{b} \frac{d[B]}{dt} \]

2. **Relate the Rates**:
From the stoichiometry of the reaction, we can relate the rates of change of A and B:
\[ -\frac{1}{a} \frac{d[A]}{dt} = -\frac{1}{b} \frac{d[B]}{dt} \]

3. **Rearranging the Equation**:
Rearranging the above equation gives us:
\[ \frac{d[A]}{dt} = -\frac{a}{b} \frac{d[B]}{dt} \]

4. **Final Expression**:
Thus, we can express the rate of change of concentration of A as:
\[ -\frac{d[A]}{dt} = \frac{a}{b} \frac{d[B]}{dt} \]

5. **Conclusion**:
Therefore, the expression for \(-\frac{d[A]}{dt}\) in terms of \(-\frac{d[B]}{dt}\) is:
\[ -\frac{d[A]}{dt} = -\frac{a}{b} \frac{d[B]}{dt} \]