Rate law of the `n^(th)` order reaction is given by `(dx)/(dt)=k[A]^(n)`
What kinetic parameters can you derive from logarithm graph

Options

A. n(order) of reaction
B. k(rate constant)
C. Both a and b
D. None of these

Explanation

To derive kinetic parameters from the logarithmic graph of the rate law for an nth order reaction given by \((dx)/(dt) = k[A]^n\), we can follow these steps:

### Step 1: Write the Rate Law
The rate law for the nth order reaction is given by:
\[ \frac{dx}{dt} = k[A]^n \]
where:
- \(\frac{dx}{dt}\) is the rate of the reaction,
- \(k\) is the rate constant,
- \([A]\) is the concentration of reactant A,
- \(n\) is the order of the reaction.

### Step 2: Take the Logarithm
To analyze this equation using a logarithmic graph, we can take the logarithm of both sides:
\[ \log\left(\frac{dx}{dt}\right) = \log(k) + n \log([A]) \]

### Step 3: Rearrange the Equation
This equation can be rearranged into the form of a straight line \(y = mx + c\):
- Let \(y = \log\left(\frac{dx}{dt}\right)\)
- Let \(x = \log([A])\)
- The slope \(m = n\)
- The y-intercept \(c = \log(k)\)

Thus, we have:
\[ \log\left(\frac{dx}{dt}\right) = n \log([A]) + \log(k) \]

### Step 4: Analyze the Graph
From the graph of \(\log\left(\frac{dx}{dt}\right)\) versus \(\log([A])\):
- The slope of the line gives the order of the reaction \(n\).
- The y-intercept gives the logarithm of the rate constant \(\log(k)\).

### Conclusion
From the logarithmic graph, we can derive:
1. The order of the reaction \(n\).
2. The rate constant \(k\).