For a reaction a graph plotted between `log(dx/dt)andlog(a-x)` along y and x axes respectively shows a straight line with a positive slope of `45^(@)`. The order of the reaction is

Options

A. 0
B. 1
C. 2
D. 3

Answer

To determine the order of the reaction from the given information, we can follow these steps:

### Step 1: Understand the relationship
The question states that a graph is plotted between `log(dx/dt)` (the logarithm of the rate of reaction) and `log(a - x)` (the logarithm of the remaining concentration of reactant). The slope of this graph is given as `45 degrees`.

### Step 2: Interpret the slope
A slope of `45 degrees` indicates that the slope is equal to `1`. In mathematical terms, this means:
\[ \text{slope} = 1 \]
This implies that:
\[ \log\left(\frac{dx}{dt}\right) = m \cdot \log(a - x) + c \]
where \( m = 1 \).

### Step 3: Relate to the rate law
For a reaction of order \( n \), the rate of reaction can be expressed as:
\[ \frac{dx}{dt} = k(a - x)^n \]
Taking logarithms on both sides gives:
\[ \log\left(\frac{dx}{dt}\right) = \log(k) + n \cdot \log(a - x) \]
This is in the form of a straight line \( y = mx + c \), where:
- \( y = \log\left(\frac{dx}{dt}\right) \)
- \( x = \log(a - x) \)
- \( m = n \) (the order of the reaction)
- \( c = \log(k) \)

### Step 4: Determine the order of the reaction
Since the slope \( m \) is equal to \( 1 \) (from the 45-degree angle), we can conclude that:
\[ n = 1 \]
This indicates that the reaction is of **first order**.

### Conclusion
Thus, the order of the reaction is **1**.

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