Question 1

The half-life of the first order radioactive decay of  is 1.30 10 9 years. How long would it take for the  to decay to 25% of its original concentration?

Accepted Answer

To find the time it takes for the sample to decay to 25% of its original concentration (i.e. 75% has decayed), we need to use the formula for first order radioactive decay:

N/N₀ = e^(-kt)

where N is the final concentration (75% of N₀), N₀ is the initial concentration, k is the decay constant (ln2/t½), and t is the time. Solving for t:

0.75 = e^(-k(1.3×10^9))

ln(0.75) = -k(1.3×10^9)

k = 5.17×10^-10

Now we can use this value of k to find t when N/N₀ = 0.25:

0.25 = e^(-5.17×10^-10 t)

ln(0.25) = -5.17×10^-10 t

t = 2.60×10^19 seconds, or about 8.24×10^11 years. Therefore, the answer is D.

Question 2

Tritium is radioactive and decays by a first order process with a half-life of 12.5 yr. If an experiment starts with 1.00×10^{- 6} mol of tritium, how much is left after 4.5 yr.?

Accepted Answer

The amount of tritium left after a certain time can be calculated using the formula for first-order decay: $N = N_0 \times (1/2)^{(t/T_{1/2})}$, where $N$ is the final amount, $N_0$ is the initial amount, $t$ is the time elapsed, and $T_{1/2}$ is the half-life. Plugging in the given values ($N_0 = 1.00 \times 10^{-6}$ mol, $t = 4.5$ years, $T_{1/2} = 12.5$ years), we find $N \approx 7.8 \times 10^{-7}$ mol.

Question 3

The reaction A + 2 B→Products was studied and found to have the rate law: Rate = k [A][B]³. By what factor will the rate increase if the concentration of B is tripled while the concentration of A is held constant?

Accepted Answer

The rate law is Rate = k [A][B]^3. If [B] is tripled, the rate increases by a factor of 3^3 = 27.

Question 4

The half-life of a zero order reaction ([A] = [A]_o - k t) is 3.15 sec for an initial concentration ([A]_o) of 0.500 M . What is the rate constant for this reaction in mol/L × s?

Accepted Answer

The half-life equation for a zero-order reaction is:

t1/2 = [A]0/2k

We are given t1/2 = 3.15 s and [A]0 = 0.500 M.

Plugging these values into the equation, we can solve for k:

3.15 s = 0.500 M / 2k

2k = 0.500 M / 3.15 s

k = (0.500 M / 3.15 s) / 2

k = 0.0794 M/s = 7.94 × 10^-2 mol/L × s

Rounding this value to three significant figures gives a rate constant of 7.94 × 10^-2 mol/L × s, which corresponds to choice C.

Question 5

For a reaction that has the rate law: Rate = k [A][B]², the units of the specific rate constant are:

Accepted Answer

The overall order of the reaction is 3 (1 from [A] and 2 from [B]). The units of k for a third-order reaction are L²/mol² × s.

Question 6

The reaction A + B→C + D has been studied and found to have the rate law: Rate = k [A]²[B]. The overall order of the reaction is:

Accepted Answer

The overall order of the reaction is the sum of the individual reaction orders. Thus, in this case, the overall order is S1+U1+P12+S1+S1+P0=3+U1. Since U1 can be any number (including zero), the overall order can range from 3 (if U1=0) to 4 (if U1=1). Therefore, the only possible answer from the choices given is C, which corresponds to a 3rd order reaction.

Question 7

The decomposition of hydrogen peroxide to water and oxygen is a first order reaction with a rate constant of 0.0410 min^{- 1}. If we start with 0.500 M H₂O₂, what will be its concentration after 10.0 minutes?

Accepted Answer

The rate law for the decomposition of hydrogen peroxide is given as:
rate = k[H2O2]
where k is the rate constant.

Since it is a first-order reaction, we can use the integrated rate law to calculate the concentration of H2O2 after 10 minutes:
ln[H2O2] = -kt + ln[H2O2]0
where [H2O2]0 is the initial concentration of H2O2

ln[H2O2] = -(0.0410 min^-1)(10.0 min) + ln(0.500 M) = -0.303

[H2O2] = e^-0.303 = 0.737 M

Therefore, the concentration of H2O2 after 10 minutes is 0.737 M. However, the question asks for the concentration of H2O2, not the reactant.

Since the reaction is stoichiometrically balanced, the concentration of H2O2 is reduced by a factor of 2 for every mole of O2 produced. Thus, the concentration of H2O2 after 10 minutes is:

[H2O2] = (0.500 M) / 2 = 0.250 M

Therefore, the best choice is C (0.332 M is incorrect because it is higher than the initial concentration).

Question 8

The y-intercept on a second order Time-Concentration plot is related to what?

Accepted Answer

The y-intercept on a second order Time-Concentration plot is related to 1/[A] at time = 0. This can be seen from the second order integrated rate law, where 1/[A] = kt + 1/[A]0. Therefore, the y-intercept is equal to 1/[A]0, which is option C.

Question 9

The reaction X + Y→Z has the rate law Rate = k [X][Y]. The units of the specific rate constant in this case are:

Accepted Answer

The rate law is Rate = k[X][Y], indicating a second-order reaction (first order in [X] and first order in [Y]). The units of k for a second-order reaction are L/(mol·s), which matches choice D.

Question 10

The gas phase reaction X + Z Q is found to have the rate law Rate =  . What will be the effect of doubling the initial pressure of both X and Z on the initial rate?

Accepted Answer

The answer of The gas phase reaction X + Z...

Question 11

The reaction A + B→C obeys the first order rate law: R = 5.75×10^{- 3} s^{- 1} [A]. What is the half-life of this reaction when the initial concentration of A is 0.40 M ?

Accepted Answer

For a first-order reaction, the half-life (t1/2) is given by the formula t1/2 = 0.693/k, where k is the rate constant. Here, k = 5.75×10^-3 s^-1. Plugging in the values, t1/2 = 0.693 / 5.75×10^-3 s^-1 = 120.52 s, which rounds to 120 s.

Question 12

A sample of the radioactive isotope ⁹⁰Sr was found to decay by a first order process. If 1.00% of the original 2.5×10^{- 3} gram sample decays in 0.406 years, determine the half-life of ⁹⁰Sr.

Accepted Answer

The answer of A sample of the radioactive isotope ⁹⁰Sr...

Question 13

Exhibit 13-13 Graphical analysis can be used to determine the rate law for a general reaction of reactant "A" going to products "B" and "C".
A→B + C
Refer to Exhibit 13-13. Which of the Time-Concentration plots shown below confirms that a particular reaction follows a zero order rate law ?

Accepted Answer

The answer of Exhibit 13-13 Graphical analysis can be used...

Question 14

The highly toxic pesticide parathion, (C₂H₅O)₂PSOC₆H₄NO₂, decomposes in the soil via a first order rate law. The rate constant for the decomposition of parathion is 0.0495 days^{- 1}. How long will it take for 50% of the parathion to decompose after it is applied to the land?

Accepted Answer

To solve this problem, we can use the first order rate law equation:

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

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

We want to find the time it takes for 50% of the parathion to decompose, which means [A]t/[A]0 = 0.5. Plugging in the values given in the problem:

ln(0.5) = -0.0495 days^-1 * t

Solving for t:

t = ln(0.5) / 0.0495 days^-1 
t ≈ 2 weeks

Therefore, the answer is B) 2 weeks.

Question 15

For the zero order rate law  = - k , the rate equation is A = A o - k t. The half-life for a zero order rate is given as:

Accepted Answer

The answer of For the zero order rate law ...

Question 16

Exhibit 13-13 Graphical analysis can be used to determine the rate law for a general reaction of reactant "A" going to products "B" and "C".
A→B + C
Refer to Exhibit 13-13. Which of the Time-Concentration plots shown below confirms that a particular reaction follows a first order rate law ?

Accepted Answer

The answer of Exhibit 13-13 Graphical analysis can be used...

Question 17

Which rate law given below corresponds to the following equation for solving for its half-life? T_1/2 = [A]_o/2 k

Accepted Answer

The answer of Which rate law given below corresponds to...

Question 18

The gas phase reaction C₂H₄ + Cl₂→C₂H₄Cl₂ follows the rate law: Rate = k [C₂H₄] [Cl₂]². If the concentration of C₂H₄ is doubled while the concentration of Cl₂ remains constant, the initial rate of the reaction:

Accepted Answer

According to the rate law, doubling the concentration of C₂H₄ while keeping the concentration of Cl₂ constant would result in the rate being proportional to [C₂H₄] x [Cl₂]² x 2 = 2[C₂H₄] x [Cl₂]². Therefore, the rate would increase by a factor of 2. The answer is C.

Question 19

What is a half-life ?

Accepted Answer

A half-life is the amount of time it takes for the concentration of a reactant to decrease by half. This means that after one half-life, the concentration will be one-half its original value, and after two half-lives, it will be one-fourth its original value, and so on. Choice B correctly describes this concept.

Question 20

A reaction in solution, A + B→P, is studied and found to have the rate law Rate = k [A] with a rate constant of 3.5×10^{- 3} s^{- 1}. If an experiment begins with a concentration of A equal to 0.20 M , at what time after the start of the experiment will the concentration of A be 0.050 M ?

Accepted Answer

We can use the integrated rate law equation for first-order reactions:

[A]t = [A]0 e^(-kt)

We can rearrange this to solve for time:

t = (-1/k)ln([A]t/[A]0)

We are given the initial concentration of A (0.20 M) and the final concentration of A (0.050 M), so we can plug these values into the equation and solve for time:

t = (-1/3.5x10^-3 s^-1)ln(0.050 M/0.20 M) = 3.9x10^2 s = 3.9x10^1 s (to 2 significant figures)

Therefore, the answer is C) 3.9x10^1 s.

Quiz 13: Chemical Kinetics

The half-life of the first order radioactive decay of is 1.30 10 9 years. How long would it take for the to decay to 25% of its original concentration?

Tritium is radioactive and decays by a first order process with a half-life of 12.5 yr. If an experiment starts with 1.00×10^{- 6} mol of tritium, how much is left after 4.5 yr.?

The reaction A + 2 B→Products was studied and found to have the rate law: Rate = k [A][B]³. By what factor will the rate increase if the concentration of B is tripled while the concentration of A is held constant?

The half-life of a zero order reaction ([A] = [A]_o - k t) is 3.15 sec for an initial concentration ([A]_o) of 0.500 M . What is the rate constant for this reaction in mol/L × s?

For a reaction that has the rate law: Rate = k [A][B]², the units of the specific rate constant are:

The reaction A + B→C + D has been studied and found to have the rate law: Rate = k [A]²[B]. The overall order of the reaction is:

The decomposition of hydrogen peroxide to water and oxygen is a first order reaction with a rate constant of 0.0410 min^{- 1}. If we start with 0.500 M H₂O₂, what will be its concentration after 10.0 minutes?

The y-intercept on a second order Time-Concentration plot is related to what?

The reaction X + Y→Z has the rate law Rate = k [X][Y]. The units of the specific rate constant in this case are:

The gas phase reaction X + Z Q is found to have the rate law Rate = . What will be the effect of doubling the initial pressure of both X and Z on the initial rate?

The reaction A + B→C obeys the first order rate law: R = 5.75×10^{- 3} s^{- 1} [A]. What is the half-life of this reaction when the initial concentration of A is 0.40 M ?

A sample of the radioactive isotope ⁹⁰Sr was found to decay by a first order process. If 1.00% of the original 2.5×10^{- 3} gram sample decays in 0.406 years, determine the half-life of ⁹⁰Sr.

Exhibit 13-13 Graphical analysis can be used to determine the rate law for a general reaction of reactant "A" going to products "B" and "C". A→B + C Refer to Exhibit 13-13. Which of the Time-Concentration plots shown below confirms that a particular reaction follows a zero order rate law ?

The highly toxic pesticide parathion, (C₂H₅O) ₂PSOC₆H₄NO₂, decomposes in the soil via a first order rate law. The rate constant for the decomposition of parathion is 0.0495 days^{- 1}. How long will it take for 50% of the parathion to decompose after it is applied to the land?

For the zero order rate law = - k , the rate equation is A = A o - k t. The half-life for a zero order rate is given as:

Exhibit 13-13 Graphical analysis can be used to determine the rate law for a general reaction of reactant "A" going to products "B" and "C". A→B + C Refer to Exhibit 13-13. Which of the Time-Concentration plots shown below confirms that a particular reaction follows a first order rate law ?

Which rate law given below corresponds to the following equation for solving for its half-life? T_1/2 = [A]_o/2 k

The gas phase reaction C₂H₄ + Cl₂→C₂H₄Cl₂ follows the rate law: Rate = k [C₂H₄] [Cl₂]². If the concentration of C₂H₄ is doubled while the concentration of Cl₂ remains constant, the initial rate of the reaction:

What is a half-life ?

A reaction in solution, A + B→P, is studied and found to have the rate law Rate = k [A] with a rate constant of 3.5×10^{- 3} s^{- 1}. If an experiment begins with a concentration of A equal to 0.20 M , at what time after the start of the experiment will the concentration of A be 0.050 M ?

Quiz 13: Chemical Kinetics

The half-life of the first order radioactive decay of is 1.30 10 9 years. How long would it take for the to decay to 25% of its original concentration?

Tritium is radioactive and decays by a first order process with a half-life of 12.5 yr. If an experiment starts with 1.00×10 - 6 mol of tritium, how much is left after 4.5 yr.?

The reaction A + 2 B→Products was studied and found to have the rate law: Rate = k [A][B]3. By what factor will the rate increase if the concentration of B is tripled while the concentration of A is held constant?

The half-life of a zero order reaction ([A] = [A]o - k t) is 3.15 sec for an initial concentration ([A]o) of 0.500 M . What is the rate constant for this reaction in mol/L × s?

For a reaction that has the rate law: Rate = k [A][B]2, the units of the specific rate constant are:

The reaction A + B→C + D has been studied and found to have the rate law: Rate = k [A]2[B]. The overall order of the reaction is:

The decomposition of hydrogen peroxide to water and oxygen is a first order reaction with a rate constant of 0.0410 min - 1. If we start with 0.500 M H2O2, what will be its concentration after 10.0 minutes?

The y-intercept on a second order Time-Concentration plot is related to what?

The reaction X + Y→Z has the rate law Rate = k [X][Y]. The units of the specific rate constant in this case are:

The gas phase reaction X + Z Q is found to have the rate law Rate = . What will be the effect of doubling the initial pressure of both X and Z on the initial rate?

The reaction A + B→C obeys the first order rate law: R = 5.75×10 - 3 s - 1 [A]. What is the half-life of this reaction when the initial concentration of A is 0.40 M ?

A sample of the radioactive isotope 90Sr was found to decay by a first order process. If 1.00% of the original 2.5×10 - 3 gram sample decays in 0.406 years, determine the half-life of 90Sr.

Exhibit 13-13 Graphical analysis can be used to determine the rate law for a general reaction of reactant "A" going to products "B" and "C". A→B + C Refer to Exhibit 13-13. Which of the Time-Concentration plots shown below confirms that a particular reaction follows a zero order rate law ?

The highly toxic pesticide parathion, (C2H5O) 2PSOC6H4NO2, decomposes in the soil via a first order rate law. The rate constant for the decomposition of parathion is 0.0495 days - 1. How long will it take for 50% of the parathion to decompose after it is applied to the land?

For the zero order rate law = - k , the rate equation is A = A o - k t. The half-life for a zero order rate is given as:

Exhibit 13-13 Graphical analysis can be used to determine the rate law for a general reaction of reactant "A" going to products "B" and "C". A→B + C Refer to Exhibit 13-13. Which of the Time-Concentration plots shown below confirms that a particular reaction follows a first order rate law ?

Which rate law given below corresponds to the following equation for solving for its half-life? T1/2 = [A]o/2 k

The gas phase reaction C2H4 + Cl2→C2H4Cl2 follows the rate law: Rate = k [C2H4] [Cl2]2. If the concentration of C2H4 is doubled while the concentration of Cl2 remains constant, the initial rate of the reaction:

What is a half-life ?

A reaction in solution, A + B→P, is studied and found to have the rate law Rate = k [A] with a rate constant of 3.5×10 - 3 s - 1. If an experiment begins with a concentration of A equal to 0.20 M , at what time after the start of the experiment will the concentration of A be 0.050 M ?

Tritium is radioactive and decays by a first order process with a half-life of 12.5 yr. If an experiment starts with 1.00×10^{- 6} mol of tritium, how much is left after 4.5 yr.?

The reaction A + 2 B→Products was studied and found to have the rate law: Rate = k [A][B]³. By what factor will the rate increase if the concentration of B is tripled while the concentration of A is held constant?

The half-life of a zero order reaction ([A] = [A]_o - k t) is 3.15 sec for an initial concentration ([A]_o) of 0.500 M . What is the rate constant for this reaction in mol/L × s?

For a reaction that has the rate law: Rate = k [A][B]², the units of the specific rate constant are:

The reaction A + B→C + D has been studied and found to have the rate law: Rate = k [A]²[B]. The overall order of the reaction is:

The decomposition of hydrogen peroxide to water and oxygen is a first order reaction with a rate constant of 0.0410 min^{- 1}. If we start with 0.500 M H₂O₂, what will be its concentration after 10.0 minutes?

The reaction A + B→C obeys the first order rate law: R = 5.75×10^{- 3} s^{- 1} [A]. What is the half-life of this reaction when the initial concentration of A is 0.40 M ?

A sample of the radioactive isotope ⁹⁰Sr was found to decay by a first order process. If 1.00% of the original 2.5×10^{- 3} gram sample decays in 0.406 years, determine the half-life of ⁹⁰Sr.

The highly toxic pesticide parathion, (C₂H₅O) ₂PSOC₆H₄NO₂, decomposes in the soil via a first order rate law. The rate constant for the decomposition of parathion is 0.0495 days^{- 1}. How long will it take for 50% of the parathion to decompose after it is applied to the land?

Which rate law given below corresponds to the following equation for solving for its half-life? T_1/2 = [A]_o/2 k

The gas phase reaction C₂H₄ + Cl₂→C₂H₄Cl₂ follows the rate law: Rate = k [C₂H₄] [Cl₂]². If the concentration of C₂H₄ is doubled while the concentration of Cl₂ remains constant, the initial rate of the reaction:

A reaction in solution, A + B→P, is studied and found to have the rate law Rate = k [A] with a rate constant of 3.5×10^{- 3} s^{- 1}. If an experiment begins with a concentration of A equal to 0.20 M , at what time after the start of the experiment will the concentration of A be 0.050 M ?