Note: Based on the standard CBSE Chemistry curriculum, the graph provided (implied by the context of the questions) is a plot of Concentration $[R]$ versus Time $t$ for a reaction where the rate is independent of concentration.
Step 1 (Governing Law & Identification): [0.5 Mark]
For a reaction where the graph of $[R]$ versus $t$ is a straight line with a negative slope, the rate law is given by:
$$Rate = -\frac{d[R]}{dt} = k[R]^0 = k$$This confirms the reaction follows Zero Order Kinetics.
Step 2 (Mathematical Working): [1.0 Mark]
- Slope Calculation: Integrating the rate law $[R]_t = -kt + [R]_0$, we compare this to the linear equation $y = mx + c$. Here, $y = [R]$, $x = t$, and the slope $m = -k$. Therefore, the slope of the curve is $-k$.
- Half-life Derivation: For a zero-order reaction, the time taken for the concentration to become half ($[R] = \frac{[R]_0}{2}$) is: $$\frac{[R]_0}{2} = -kt_{1/2} + [R]_0$$ $$kt_{1/2} = \frac{[R]_0}{2}$$ $$t_{1/2} = \frac{[R]_0}{2k}$$
Step 3 (Final Concluded Answer): [0.5 Mark]
- Order of reaction: Zero order ($n=0$).
- Slope of the curve: $-k$ (where $k$ is the rate constant).
- Relationship between $k$ and $t_{1/2}$: $$k = \frac{[R]_0}{2t_{1/2}}$$
💡 EL10 Concept Insight: Think of a zero-order reaction like a tap dripping at a constant speed regardless of how much water is left in the tank. Because the speed never changes, the time it takes to empty half the tank depends entirely on how much water you started with!