Question

Most of the time, the rate of a reaction depends on the concentration of the reactant. In the case of second-order reactions, the rate is proportional to the square of the concentration of the reactant.

Select the image to explore the simulation, which will help you to understand how second-order reactions are identified by the nature of their plots. You can also observe the rate law for different reactions.

2HIHI Ralewa -64-10ml) 500K Initial rate-1.6-10 ml ) 01010 time 10 Mot T ime OPHT ime OPHT ime 21- 19

In the simulation, you can select one of the three different kinds of plots. You may use the Start , Stop, and Reset buttons to observe the corresponding changes in the plot for different kinds of reactions. You can also select six different reactions using the drop-down menu and observe three different types of plots for each reaction.

Relating plots to the order of a reaction

Consider the following reaction:

A→products

The plot of [A] versus t is linear for the zero-order reaction, the plot of ln[A] versus t is linear for the first-order reaction, and the plot of 1[A] versus t is linear for the second-order reaction. [A] represents the concentration of the reactant A.

Reaction order	Linear plot
zero	[A] vs. t
first	ln[A] vs. t
second	1[A] vs. t

The linearity of each graph can be used to identify the order of a reaction.

Characteristics of second-order reactions

For a second-order reaction, [A]→products, the rate of the reaction is given as rate= k[A]2, where k is the rate constant and [A] is the concentration of reactant A. The integrated rate law for second-order reactions is 1[A]t=kt+1[A]0, where [A]t is the concentration of reactant A at time t, k is the rate constant, and [A]0 is the initial concentration of reactant A. This equation is of the type y=mx+b. Therefore, the plot of 1[A]t versus time is always a straight line with a slope k and a y intercept 1[A]0.

Part B

Consider the second-order reaction:

2HI(g)→H2(g)+I2(g)

Use the simulation to find the initial concentration [HI]0 and the rate constant k for the reaction. What will be the concentration of HI after t = 6.82×10¹⁰ s ([HI]t) for a reaction starting under the condition in the simulation?

Express your answer in moles per liters to three significant figures.

Answer 1

2 K The second order rate equation, rate = K[A] [A]”- rate 10. [A] - podle at initial position, (where ro is the initial rate of [A]- V Ř C he reaction) :.: 11.6X101 ** [a]. - Vi har og 6.4 x 10-9.. a. [A]o - s tew for second os for second order reaction in rate law . Now, the integrated De • kt * CM) 3 64x10-7X 6-82x10'0x + or 5 436-68 og [A] 4 = 2.29 X10-3 So, [A]{ = 2.29.7.10-3 moles per litre.