Question

Slope of the graph between rate (Y-axis) and [A] (X-axis) for the first order reaction is equal to

• A. $k$
• B. $\frac{2.303}{k}$
• C. $\frac{k}{2.303}$
• D. $-k$

Hint:

If the reaction were zero-order, the rate law would be $\text{Rate} = k[\text{A}]^0 = k$. The graph of Rate vs [A] would be a flat, horizontal line with a slope of exactly zero!

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks for the mathematical slope of a specific plot: Rate versus Concentration of reactant A ($[\text{A}]$) for a strictly first-order chemical reaction.

Step 2: Key Formula or Approach:
The differential rate law for a first-order reaction $A \rightarrow \text{Products}$ is expressed as:
$$\text{Rate} = k[\text{A}]^1$$
Where $k$ is the specific rate constant.

Step 3: Detailed Explanation:
We can map this rate equation to the standard equation of a straight line, which is $y = mx + c$.
Here, $y$ is the Rate (plotted on the Y-axis), and $x$ is the concentration $[\text{A}]$ (plotted on the X-axis).
$$\text{Rate} = k \cdot [\text{A}] + 0$$
$$y = m \cdot x + c$$
By directly comparing the two equations, we can see that the y-intercept ($c$) is $0$, meaning the line passes through the origin.
The slope ($m$) directly corresponds to the rate constant $k$.

Step 4: Final Answer:
The slope of the graph is equal to $k$, which corresponds to option (A).