Question

The half life of a first order reaction is 10 min. In what time, the rate of reaction will decreases from 6.0×10²¹ moleculed ml⁻¹ s⁻¹ to 4.5×10²⁵ mdecules l⁻¹ m⁻¹ (NA​=6.0×10²³)

a. 10 min
b. 20 min
c. 30 min
d. 40 min

Answer 1

The time it takes for the rate of reaction to decrease from 6.0×10²¹ molecules ml⁻¹ s⁻¹ to 4.5×10²⁵ molecules l⁻¹ m⁻¹ is 30 minutes. The correct answer is option c.

Step-by-step explanation:

The half-life of a first-order reaction can be found using the formula t₁/₂ = 0.693/k, where t₁/₂ is the half-life and k is the rate constant. In this case, the half-life of the reaction is 10 minutes. To find the time it takes for the reaction rate to decrease from 6.0×10²¹ molecules ml⁻¹ s⁻¹ to 4.5×10²⁵ molecules l⁻¹ m⁻¹.

We need to determine how many half-lives it takes for the concentration to decrease to the desired value. First, we need to calculate the initial concentration in molecules ml⁻¹. Using Avogadro's number (NA​=6.0×10²³), we can convert the given concentrations to molecules ml⁻¹.

Then, we can use the formula t = n * t₁/₂, where t is the time needed, n is the number of half-lives, and t₁/₂ is the half-life. Substituting the values into the equation, we find that it takes 30 minutes for the rate of reaction to decrease from 6.0×10²¹ molecules ml⁻¹ s⁻¹ to 4.5×10²⁵ molecules l⁻¹ m⁻¹.