Consider the reaction represented by the equation 2 X + 2 Z → X2Z2. During a reaction in which a lar — Kinetics Chemistry Question

STEPS:

1. Understand the kinetic conditions (Pseudo-order conditions): The reaction is given as $2\text{ X} + 2\text{ Z} \rightarrow \text{X}_2\text{Z}_2$. The problem states that reactant X is present in large excess. When a reactant is in massive excess, its concentration remains virtually constant throughout the reaction ($[\text{X}]_t \approx [\text{X}]_0$). This simplifies the overall rate law so that any changes in the reaction rate are solely due to changes in the concentration of reactant Z, allowing us to determine Z's reaction order directly from the integrated rate law plots.
2. Recall the graphical relationships of integrated rate laws: Under these conditions, we can identify the reaction order with respect to Z by looking at which plot yields a straight line:
* Zero-order: A plot of concentration versus time, $[\text{Z}]$ vs. $t$, is a straight line: $[\text{Z}]_t = -kt + [\text{Z}]_0$.
* First-order: A plot of the natural logarithm of concentration versus time, $\ln[\text{Z}]$ vs. $t$, is a straight line: $\ln[\text{Z}]_t = -kt + \ln[\text{Z}]_0$.
* Second-order: A plot of the reciprocal of concentration versus time, $1/[\text{Z}]$ vs. $t$, is a straight line: $1/[\text{Z}]_t = kt + 1/[\text{Z}]_0$.
3. Analyze the provided graph: The vertical axis of the graph is labeled $\ln[\text{Z}]$ and the horizontal axis is labeled Time. The data plotted forms a straight, downward-sloping linear line with a constant slope.
4. Determine the reaction order: Since the plot of $\ln[\text{Z}]$ versus time is linear, the reaction must be first order with respect to reactant Z. The slope of this line corresponds to $-k$ (the negative of the rate constant). This identifies Option B as the correct choice.

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WHY_OTHERS_WRONG:

• Option A is incorrect: For a zero-order reaction, a plot of the raw concentration over time ($[\text{Z}]$ vs. $t$) is linear. If you plot the natural logarithm of concentration over time for a zero-order reaction, the graph will curve downward rather than forming a straight line.
• Option C is incorrect: For a second-order reaction, a plot of the reciprocal of concentration over time ($1/[\text{Z}]$ vs. $t$) yields a linear relationship with a positive slope. A plot of $\ln[\text{Z}]$ vs. $t$ for a second-order reaction will bend and flatten out over time.
• Option D is incorrect: A third-order reaction is extremely rare and would require a linear relationship on a plot of $1/[\text{Z}]^2$ vs. $t$, which does not correspond to the linear logarithmic plot shown.