For a first-order reaction R P at a given temperature, k is the rate constant. For this reaction, at the given temperature, the concentrations of R and P at a time t are [ R ] and [ P ], respectively. The correct graphical representation(s) for this reaction is(are)
D.
For a first-order reaction R P , the rate law is given by: - d [ R ] d t = d [ P ] d t = k[ R ] Integrating this, the concentration of the reactant at time t is [ R ] = [ R ]_0 e^ -kt . The concentration of the product at time t is [ P ] = [ R ]_0 - [ R ] = [ R ]_0 (1 - e^ -kt ). The plot of [ P ] versus t follows the equation [ P ] = [ R ]_0 (1 - e^ -kt ). This represents a curve that starts from the origin and is concave down, approaching a constant value [ R ]_0. The graph in (A) is concave up, making it incorrect. The plot of d [ R ] d t versus [ R ] follows the equation d [ R ] d t = -k[ R ]. This is a straight line passing through the origin with a negative slope (-k). The graph in (B) has a positive slope, making it incorrect. The plot of d [ P ] d t versus t follows the equation d [ P ] d t = k[ R ]_0 e^ -kt . This represents an exponentially decreasing curve with respect to time. The graph in (C) matches this behavior, making it correct. The rate constant k depends only on the temperature and is independent of time. Therefore, the plot of k versus t is a horizontal straight line. The graph in (D) matches this, making it correct. Answer: ;
Related: Chemistry — Chemical Kinetics · All PYQ Banks