For a chemical reaction \( R \to P \), the variation in the concentration \([R]\) vs time \( t \) plot is given as: (a) Predict the order of the reaction and write the unit of rate constant (\( k \)) for this order of reaction.
(b) What is the slope of the curve?
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For a zero-order reaction, the rate is independent of reactant concentration, and the half-life is given by:
\[
t_{1/2} = \frac{[R]_0}{2k}
\]
(a) Reaction Order and Rate Constant Unit: The linear relationship with a negative slope observed in the plot of concentration \([R]\) versus time \( t \) indicates that the reaction proceeds with zero-order kinetics. For a zero-order reaction, the integrated rate law is given by: \[[R] = [R]_0 - kt\]Here, \( k \) represents the rate constant. The unit for the rate constant of a zero-order reaction is: \[\text{mol L}^{-1} \text{s}^{-1} \quad \text{or} \quad \text{mol L}^{-1} \text{t}^{-1}\] (b) Slope of the Concentration-Time Plot: Based on the equation \( [R] = [R]_0 - kt \), the plot of \( [R] \) against \( t \) yields a straight line whose slope is equal to \( -k \). Therefore, the slope of the curve is \( -k \).
