Question

Which plot of ln k vs \(\frac{1}{T}\) is consistent with Arrhenius equation?

• A.

  

• B.

  

• C.

  

• D.

  

Answer 1

The Correct Option is D

1. The Arrhenius equation is: $\ln k = -\frac{E_a}{R} \times \frac{1}{T} + \ln A$ 

2. A plot of $\ln k$ vs $\frac{1}{T}$ yields a straight line with a negative slope ($-E_a/R$). 

3. The graph is linear and decreases as $\frac{1}{T}$ increases.

Answer 2

Step 1: Recall the Arrhenius Equation 

The Arrhenius equation is given by:

$$ k = A e^{-\frac{E_a}{RT}} $$

Taking the natural logarithm on both sides:

$$ \ln k = \ln A - \frac{E_a}{R} \cdot \frac{1}{T} $$

This equation is in the form of a straight-line equation:

$$ y = mx + c $$

where:

• \( y = \ln k \) (dependent variable)
• \( x = \frac{1}{T} \) (independent variable)
• \( m = -\frac{E_a}{R} \) (slope)
• \( c = \ln A \) (y-intercept)

Step 2: Analyze the Slope

From the equation:

• A plot of \(\ln k\) (y-axis) vs \(\frac{1}{T}\) (x-axis) should be a straight line with a negative slope \( (-E_a/R) \).
• The correct plot should show a downward linear trend.

Step 3: Identify the Correct Plot

Among the given options, only Plot 3 shows a linear decrease, which matches the Arrhenius equation.

Conclusion

The correct answer is: Plot 3.