Question

ozone (O₃) decomposes to oxygen (O₂) in the presence of chlorine atoms. the reaction follows first-order kinetics. if the initial concentration of ozone is 0.15 m and the concentration after 18.3 seconds is 0.033 m, what is the rate constant (in units of s⁻¹)?

Answer 1

To calculate the rate constant for the first-order decomposition of ozone (O₃) into oxygen (O₂), the natural logarithm of the ratio of final to initial concentration divided by the time passed is used. The calculated rate constant is 0.0827 s⁻¹.

Step-by-step explanation:

The reaction of ozone (O₃) decomposing into oxygen (O₂) in the presence of chlorine atoms is a process that follows first-order kinetics. To determine the rate constant (k) for this reaction, we use the integrated first-order rate law:\

ln([A]t/[A]0) = -kt

where:

• [A]t is the concentration of ozone at time t,
• [A]0 is the initial concentration of ozone,
• k is the rate constant,
• t is the time that has passed.

Given the initial concentration of ozone as 0.15 M and the concentration after 18.3 seconds as 0.033 M, we can substitute these values into the equation:

ln(0.033/0.15) = -18.3k

By calculating the natural logarithm, we can then solve for k:

ln(0.033/0.15) = -18.3k

= ln(0.22) = -18.3k

= -1.5143 = -18.3k

k = 0.0827 s⁻¹

The rate constant for the decomposition of ozone into oxygen is 0.0827 s⁻¹.