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?
Show Hint
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) Order of the Reaction and Unit of Rate Constant:
Since the plot of concentration \([R]\) versus time \( t \) is a straight line with a negative slope, the reaction follows zero-order kinetics.
For a zero-order reaction:
\[
[R] = [R]_0 - kt
\]
where \( k \) is the rate constant.
The unit of the rate constant for 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 Curve:
From the equation \( [R] = [R]_0 - kt \), the plot of \( [R] \) vs. \( t \) has a slope of \( -k \).
Thus, the slope of the curve is \( -k \).
