The relation between the rate of a simple reaction and the concentration 'c' of the reacting species is given as

Options

A. `rate propto c`
B. `rate propto 1/c`
C. `rate propto 1/c^(n)`
D. `rate propto c^(n)` (n = order of reaction)

Answer

To solve the question regarding the relationship between the rate of a simple reaction and the concentration 'c' of the reacting species, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Reaction Rate**: The rate of a chemical reaction is generally defined as the change in concentration of a reactant or product per unit time. For a simple reaction, we can denote it as:
\[ \text{Rate} = -\frac{d[A]}{dt} \]
where \([A]\) is the concentration of the reactant A.

2. **Proportionality to Concentration**: The rate of a reaction can be expressed in terms of the concentration of the reactants. The general form is:
\[ \text{Rate} \propto [A]^n \]
where \(n\) is the order of the reaction with respect to reactant A.

3. **Removing Proportionality**: To convert the proportionality into an equation, we introduce a rate constant \(k\):
\[ \text{Rate} = k[A]^n \]

4. **Identifying the Order of Reaction**: The exponent \(n\) in the equation indicates the order of the reaction. It can be determined experimentally and is not necessarily equal to the stoichiometric coefficients in the balanced equation.

5. **Analyzing Given Options**: The question provides several options regarding the relationship between rate and concentration:
- Rate is directly proportional to concentration \(c\)
- Rate is directly proportional to \(\frac{1}{c}\)
- Rate is directly proportional to \(\frac{1}{c^n}\)
- Rate is directly proportional to \(c^n\)

Based on our understanding, the correct relationship is that the rate is directly proportional to the concentration of the reactant raised to the power of its order, which is \(c^n\).

6. **Conclusion**: Therefore, the correct answer is:
\[ \text{Rate} \propto c^n \]
This corresponds to option D.