Question 1

The rate constant for the first-order decomposition of N₂O is 3.40 s^-1.What is the half-life of the decomposition?

Accepted Answer

The first-order rate equation is given by: 
ln([A]t/[A]0) = -kt
where [A]t is the concentration at time t, [A]0 is the initial concentration, k is the rate constant and t is time.
For first order reaction t1/2 = ln(2)/k
Substituting the given values in the above equation, 
t1/2 = ln(2)/3.40s-1 = 0.2039 s ≈ 0.204 s (rounded to three significant figures)
Therefore, the answer is B.

Question 2

The rate constant for a second-order reaction is 0.54 L mol^-1s^-1.What is the half-life of this reaction if the initial concentration is 0.27 mol L^-1?

Accepted Answer

The answer of The rate constant for a second-order reaction...

Question 3

The half-life for the second-order decomposition of HI is 15.4 s when the initial concentration of HI is 0.67 mol L^-1.What is the rate constant for this reaction?

Accepted Answer

The answer of The half-life for the second-order decomposition of...

Question 4

The half-life for the decay of radium is 1620 years.What is the rate constant for this first-order process?

Accepted Answer

The answer of The half-life for the decay of radium...

Question 5

The first-order decomposition of N₂O₅ at 328 K has a rate constant of 1.70 × 10^-3 s^-1.If the initial concentration of N₂O₅ is 2.88 mol L^-1,what is the concentration of N₂O₅ after 12.5 minutes?

Accepted Answer

The answer of The first-order decomposition of N₂O₅ at 328...

Question 6

Which of the following reactions would you predict to have the smallest orientation factor?

Accepted Answer

The answer of Which of the following reactions would you...

Question 7

Derive an expression for a "1/4-life" for a first-order reaction.

Accepted Answer

The half-life of a first-order reaction is given by:
t1/2 = ln(2)/k
To find the "1/4-life", we need to determine the time it takes for the concentration of A to decrease to 1/4 of its initial value. Let's call this time t1/4:
[A]t1/4 = [A]0/4 = [A]0/2^2
Using the first-order rate law, we can write:
[A]t = [A]0e^-kt
Substituting [A]t1/4 and [A]0/2^2 for [A]t and [A]0, respectively, we get:
[A]0/2^2 = [A]0e^-kt1/4
Simplifying, we get:
1/2^2 = e^-kt1/4
ln(1/2^2) = -kt1/4
ln(4) = kt1/4
t1/4 = ln(4)/k
Now, we can substitute the expression for ln(2)/k from the equation for t1/2:
t1/4 = ln(4)/k = (2ln(2))/k = 1.386/k
Therefore, the best choice is E.

Question 8

How many half-lives are required for the concentration of reactant to decrease to 1.56% of its original value?

Accepted Answer

The answer of How many half-lives are required for the...

Question 9

The rate constant for a zero-order reaction is 0.54 L mol^-1s^-1.What is the half-life of this reaction if the initial concentration is 0.27 mol L^-1?

Accepted Answer

In a zero-order reaction, the concentration of the reactant decreases linearly over time. The half-life (t1/2) is the time taken for the initial concentration to decrease by half.

The equation for a zero-order reaction is: 
[A] = [A]0 - kt

Where:
[A]0 = initial concentration of A
[A] = concentration of A at time t
k = rate constant

To find the half-life, we need to rearrange the equation to solve for t when [A] = 0.5[A]0:

0.5[A]0 = [A]0 - kt
kt = 0.5[A]0
t = 0.5[A]0/k

Plugging in the given values:

t = 0.5(0.27 mol L-1) / 0.54 L mol-1 s-1 = 0.25 s

Therefore, the correct answer is C) 0.25 s.

Question 10

The second-order decomposition of NO₂ has a rate constant of 0.255 L mol^-1s^-1.How much NO₂ decomposes in 4.00 s if the initial concentration of NO₂ (1.00 L volume)is 1.33 mol L^-1?

Accepted Answer

The second-order rate law can be written as: Rate = k[NO₂]^2 where k = 0.255 L mol^-1s^-1. To solve for the amount of decomposition in 4.00 s, we can use the integrated rate law for a second-order reaction: 1/[NO₂]t - 1/[NO₂]0 = kt where [NO₂]t is the concentration of NO₂ at time t, [NO₂]0 is the initial concentration, and k is the rate constant. Plugging in the given values: 1/[NO₂]t - 1/[NO₂]0 = (0.255 L mol^-1s^-1)(4.00 s) 1/[NO₂]t - 1/1.33 mol L^-1 = 1.02 mol^-1S1L-P1 Solving for [NO₂]t: [NO₂]t = 0.77 mol L^-1 Therefore, the amount of NO₂ that decomposes is: [NO₂]0 - [NO₂]t = 1.33 mol L^-1 - 0.77 mol L^-1 = 0.56 mol The answer is D.

Question 11

The first-order decomposition of cyclopropane has a rate constant of 6.7 × 10^-4 s^-1.If the initial concentration of cyclopropane is 1.33 mol L^-1,what is the concentration of cyclopropane after 644 s?

Accepted Answer

The answer of The first-order decomposition of cyclopropane has a...

Question 12

If the concentration of a reactant is 6.25%,how many half-lives has it gone through?

Accepted Answer

To determine the number of half-lives, we need to use the formula:

concentration final = concentration initial x (1/2)^(number of half-lives)

Rearranging the formula, we get:

number of half-lives = log (concentration final / concentration initial) / log (1/2)

Plugging in the values, we get:

number of half-lives = log (0.0625/1) / log (1/2) = 4

Therefore, the answer is D, which corresponds to 4 half-lives.

Question 13

The first-order decay of radon has a half-life of 3.823 days.How many grams of radon remain after 7.22 days if the sample initially weighs 250.0 grams?

Accepted Answer

The answer of The first-order decay of radon has a...

Question 14

The first-order decay of radon has a half-life of 3.823 days.How many grams of radon decomposes after 5.55 days if the sample initially weighs 100.0 grams?

Accepted Answer

The answer of The first-order decay of radon has a...

Question 15

The second-order decomposition of HI has a rate constant of 1.80 × 10^-3 L mol^-1s^-1.How much HI remains after 27.3 s if the initial concentration of HI is 4.78 mol L^-1?

Accepted Answer

The answer of The second-order decomposition of HI has a...

Question 16

The first-order decomposition of N₂O at 1000 K has a rate constant of 0.76 s^-1.If the initial concentration of N₂O is 10.9 mol L^-1,what is the concentration of N₂O after 9.6 s?

Accepted Answer

The integrated rate law for first-order reactions is given by: ln([A]/[A]0) = -kt where [A] is the concentration at time t, [A]0 is the initial concentration, k is the rate constant, and t is time. Plugging in the given values, we get: ln([A]/[A]0) = -0.76(9.6) ln([A]/10.9) = -7.296 ln([A]) - ln(10.9) = -7.296 ln([A]) = -7.296 + ln(10.9) [A] = e^(-7.296 + ln(10.9)) [A] = 7.4 × 10^-3 mol/L Since the initial concentration was given in mol/L, the answer should be converted to mol: [A] = 7.4 × 10^-3 mol/L × 10.9 mol = 7.4 × 10^-3 × 10.9 mol [A] = 8.066 × 10^-2 mol Therefore, the concentration of N₂O after 9.6 s is 7.4 × 10^-3 mol/L or 8.066 × 10^-2 mol. Choice A is the best answer.

Question 17

Derive an expression for a "1/3-life" for a first-order reaction.

Accepted Answer

For a first-order reaction, the time taken for the concentration to reduce to one-third of its initial value can be derived using the formula $ t = \frac{\ln(\text{initial concentration}/\text{final concentration})}{k} $. For a "1/3-life", the final concentration is $1/3$ of the initial, so $ t = \frac{\ln(3)}{k} \approx \frac{1.099}{k} $.

Question 18

The rate constant for a first-order reaction is 0.54 L mol^-1s^-1.What is the half-life of this reaction if the initial concentration is 0.27 mol L^-1?

Accepted Answer

The answer of The rate constant for a first-order reaction...

Question 19

Which of the following reactions would you predict to have the largest orientation factor?

Accepted Answer

The answer of Which of the following reactions would you...

Question 20

For a reaction,what generally happens if the temperature is increased?

Accepted Answer

An increase in temperature generally increases the rate constant (k) of a reaction, which results in a faster reaction rate. This is due to an increase in the frequency and energy of collisions between reactant molecules, which leads to a higher probability of successful collisions and product formation.

Quiz 13: Chemical Kinetics

The rate constant for the first-order decomposition of N₂O is 3.40 s^-1.What is the half-life of the decomposition?

The rate constant for a second-order reaction is 0.54 L mol^-1s^-1.What is the half-life of this reaction if the initial concentration is 0.27 mol L^-1?

The half-life for the second-order decomposition of HI is 15.4 s when the initial concentration of HI is 0.67 mol L^-1.What is the rate constant for this reaction?

The half-life for the decay of radium is 1620 years.What is the rate constant for this first-order process?

The first-order decomposition of N₂O₅ at 328 K has a rate constant of 1.70 × 10^-3 s^-1.If the initial concentration of N₂O₅ is 2.88 mol L^-1,what is the concentration of N₂O₅ after 12.5 minutes?

Which of the following reactions would you predict to have the smallest orientation factor?

Derive an expression for a "1/4-life" for a first-order reaction.

How many half-lives are required for the concentration of reactant to decrease to 1.56% of its original value?

The rate constant for a zero-order reaction is 0.54 L mol^-1s^-1.What is the half-life of this reaction if the initial concentration is 0.27 mol L^-1?

The second-order decomposition of NO₂ has a rate constant of 0.255 L mol^-1s^-1.How much NO₂ decomposes in 4.00 s if the initial concentration of NO₂ (1.00 L volume) is 1.33 mol L^-1?

The first-order decomposition of cyclopropane has a rate constant of 6.7 × 10^-4 s^-1.If the initial concentration of cyclopropane is 1.33 mol L^-1,what is the concentration of cyclopropane after 644 s?

If the concentration of a reactant is 6.25%,how many half-lives has it gone through?

The first-order decay of radon has a half-life of 3.823 days.How many grams of radon remain after 7.22 days if the sample initially weighs 250.0 grams?

The first-order decay of radon has a half-life of 3.823 days.How many grams of radon decomposes after 5.55 days if the sample initially weighs 100.0 grams?

The second-order decomposition of HI has a rate constant of 1.80 × 10^-3 L mol^-1s^-1.How much HI remains after 27.3 s if the initial concentration of HI is 4.78 mol L^-1?

The first-order decomposition of N₂O at 1000 K has a rate constant of 0.76 s^-1.If the initial concentration of N₂O is 10.9 mol L^-1,what is the concentration of N₂O after 9.6 s?

Derive an expression for a "1/3-life" for a first-order reaction.

The rate constant for a first-order reaction is 0.54 L mol^-1s^-1.What is the half-life of this reaction if the initial concentration is 0.27 mol L^-1?

Which of the following reactions would you predict to have the largest orientation factor?

For a reaction,what generally happens if the temperature is increased?

Quiz 13: Chemical Kinetics

The rate constant for the first-order decomposition of N2O is 3.40 s-1.What is the half-life of the decomposition?

The rate constant for a second-order reaction is 0.54 L mol-1 s-1.What is the half-life of this reaction if the initial concentration is 0.27 mol L-1?

The half-life for the second-order decomposition of HI is 15.4 s when the initial concentration of HI is 0.67 mol L-1.What is the rate constant for this reaction?

The half-life for the decay of radium is 1620 years.What is the rate constant for this first-order process?

The first-order decomposition of N2O5 at 328 K has a rate constant of 1.70 × 10-3 s-1.If the initial concentration of N2O5 is 2.88 mol L-1,what is the concentration of N2O5 after 12.5 minutes?

Which of the following reactions would you predict to have the smallest orientation factor?

Derive an expression for a "1/4-life" for a first-order reaction.

How many half-lives are required for the concentration of reactant to decrease to 1.56% of its original value?

The rate constant for a zero-order reaction is 0.54 L mol-1 s-1.What is the half-life of this reaction if the initial concentration is 0.27 mol L-1?

The second-order decomposition of NO2 has a rate constant of 0.255 L mol-1 s-1.How much NO2 decomposes in 4.00 s if the initial concentration of NO2 (1.00 L volume) is 1.33 mol L-1?

The first-order decomposition of cyclopropane has a rate constant of 6.7 × 10-4 s-1.If the initial concentration of cyclopropane is 1.33 mol L-1,what is the concentration of cyclopropane after 644 s?

If the concentration of a reactant is 6.25%,how many half-lives has it gone through?

The first-order decay of radon has a half-life of 3.823 days.How many grams of radon remain after 7.22 days if the sample initially weighs 250.0 grams?

The first-order decay of radon has a half-life of 3.823 days.How many grams of radon decomposes after 5.55 days if the sample initially weighs 100.0 grams?

The second-order decomposition of HI has a rate constant of 1.80 × 10-3 L mol-1 s-1.How much HI remains after 27.3 s if the initial concentration of HI is 4.78 mol L-1?

The first-order decomposition of N2O at 1000 K has a rate constant of 0.76 s-1.If the initial concentration of N2O is 10.9 mol L-1,what is the concentration of N2O after 9.6 s?

Derive an expression for a "1/3-life" for a first-order reaction.

The rate constant for a first-order reaction is 0.54 L mol-1 s-1.What is the half-life of this reaction if the initial concentration is 0.27 mol L-1?

Which of the following reactions would you predict to have the largest orientation factor?

For a reaction,what generally happens if the temperature is increased?

The rate constant for the first-order decomposition of N₂O is 3.40 s^-1.What is the half-life of the decomposition?

The rate constant for a second-order reaction is 0.54 L mol^-1s^-1.What is the half-life of this reaction if the initial concentration is 0.27 mol L^-1?

The half-life for the second-order decomposition of HI is 15.4 s when the initial concentration of HI is 0.67 mol L^-1.What is the rate constant for this reaction?

The first-order decomposition of N₂O₅ at 328 K has a rate constant of 1.70 × 10^-3 s^-1.If the initial concentration of N₂O₅ is 2.88 mol L^-1,what is the concentration of N₂O₅ after 12.5 minutes?

The rate constant for a zero-order reaction is 0.54 L mol^-1s^-1.What is the half-life of this reaction if the initial concentration is 0.27 mol L^-1?

The second-order decomposition of NO₂ has a rate constant of 0.255 L mol^-1s^-1.How much NO₂ decomposes in 4.00 s if the initial concentration of NO₂ (1.00 L volume) is 1.33 mol L^-1?

The first-order decomposition of cyclopropane has a rate constant of 6.7 × 10^-4 s^-1.If the initial concentration of cyclopropane is 1.33 mol L^-1,what is the concentration of cyclopropane after 644 s?

The second-order decomposition of HI has a rate constant of 1.80 × 10^-3 L mol^-1s^-1.How much HI remains after 27.3 s if the initial concentration of HI is 4.78 mol L^-1?

The first-order decomposition of N₂O at 1000 K has a rate constant of 0.76 s^-1.If the initial concentration of N₂O is 10.9 mol L^-1,what is the concentration of N₂O after 9.6 s?

The rate constant for a first-order reaction is 0.54 L mol^-1s^-1.What is the half-life of this reaction if the initial concentration is 0.27 mol L^-1?