Question 1

What is the decay constant for a radioactive isotope which decreases to 34% of its original value in 2.48 hours?

Accepted Answer

We can use the formula for radioactive decay:

N = N0 * e^(-λt)

Where N0 is the initial quantity, N is the quantity at time t, λ is the decay constant, and e is the base of natural logarithms.

We are given that the quantity of the isotope decreases to 34% of its original value, so:

N/N0 = 0.34

0.34 = e^(-λt)

Taking the natural logarithm of both sides:

ln(0.34) = -λt

Solving for λ:

λ = -ln(0.34)/t

λ = 0.435 hr^-1

Therefore, the answer is (C) 0.435 hr^-1.

Question 2

An experiment with ⁵⁵Co takes 47.5 hours.At the end of the experiment,1.90 ng of ⁵⁵Co remains.If the half life is 18.0 hours,how many ng of ⁵⁵Co were originally present?

Accepted Answer

The half life of ⁵⁵Co is 18 hours. This means that every 18 hours, the amount of ⁵⁵Co is reduced by half. We can use this information to set up an equation: amount remaining = (original amount) x (1/2)^(number of half lives) We know that the experiment took 47.5 hours, which is 2.64 half lives (since 18 x 2 = 36 and 18 x 3 = 54, so it must be between 2 and 3 half lives). We also know that 1.90 ng remained at the end of the experiment. 1.90 ng = (original amount) x (1/2)^(2.64) Solving for the original amount: original amount = 11.8 ng Therefore, the answer is D) 11.8 ng.

Question 3

Fluorine-18 is a radioisotope widely used in positron emission tomography to investigate brain activity.The half-life is 109.8 minutes.How long will it take for 2.75 μg of ¹⁸F to decay to 500 ng?

Accepted Answer

First, we need to find the decay constant for Fluorine-18 using the formula:

λ = ln(2) / T(1/2)

where λ is the decay constant and T(1/2) is the half-life.

λ = ln(2) / 109.8 min = 0.0063072 min^-1

Next, we can use the formula for radioactive decay:

N = N0 * e^(-λt)

where N0 is the initial amount, N is the final amount, and t is the time elapsed.

We want to solve for t when N = 500 ng and N0 = 2.75 μg = 2750 ng.

500 = 2750 * e^(-0.0063072t)

Taking the natural log of both sides:

ln(500/2750) = -0.0063072t

Solving for t:

t = ln(500/2750) / -0.0063072 = 270.2 min

Therefore, it will take approximately 270 min for 2.75 μg of Fluorine-18 to decay to 500 ng. The best choice is B.

Question 4

Iodine-123,used in thyroid therapy,has a half-life of 13.27 hours.How many half-lives are required for a 160 mg sample of iodine-123 to decay to 5.0 mg?

Accepted Answer

The amount of iodine-123 left after n half-lives can be calculated using the formula:

Amount remaining = (initial amount) x (1/2)^n

Let's plug in the values given in the problem:

(5.0 mg) = (160 mg) x (1/2)^n

Solving for n:

(1/2)^n = (5.0 mg)/(160 mg)
(1/2)^n = 0.03125

Taking the log of both sides:

n*log(1/2) = log(0.03125)
n*(-0.301) = -1.505
n = 5

Therefore, it would take 5 half-lives for a 160 mg sample of iodine-123 to decay to 5.0 mg.

Question 5

The first-order reaction,SO₂Cl₂ → SO₂ + Cl₂,has a half-life of 8.75 hours at 593 K.How long will it take for the concentration of SO₂Cl₂ to fall to 12.5% of its initial value?

Accepted Answer

Given, k = 0.079 (using half-life formula) We know, for a first-order reaction, the rate constant can be calculated using the following equation: k = (ln (A0/At)) / t where A0 is the initial concentration and At is the concentration after time t. Let t be the time for the concentration to fall to 12.5% of its initial value. Then, At = 0.125 A0 and we can rewrite the above equation as: t = (ln (A0/At)) / k t = (ln (1/0.125)) / 0.079 t = 26.2 hours Therefore, the time required for the concentration of SO₂Cl₂ to fall to 12.5% of its initial value is 26.2 hours. Hence, option D is the correct answer.

Question 6

The isomerization reaction,CH₃NC → CH₃CN,is first order and the rate constant is equal to 0)46 s^-1 at 600 K.What is the concentration of CH₃NC after 0.20 minutes if the initial concentration is 0.10 M?

Accepted Answer

The rate law for a first-order reaction is: rate = k[A], where k is the rate constant and [A] is the concentration of the reactant. The integrated rate law for a first-order reaction is: ln[A]t = -kt + ln[A]0, where [A]t is the concentration of the reactant at time t, [A]0 is the initial concentration of the reactant, and k is the rate constant. We can use this equation to calculate the concentration of CH3NC after 0.20 minutes if the initial concentration is 0.10 M.ln[CH3NC]t = -k*t + ln[CH3NC]0ln[CH3NC]t = -(46 s^-1)*(0.20 min)*(60 s/min) + ln(0.10 M)ln[CH3NC]t = -5.52[CH3NC]t = 0.004 MTherefore, the concentration of CH3NC after 0.20 minutes if the initial concentration is 0.10 M is 0.004 M.

Question 7

The half life of the reaction shown below is found not to depend on the concentration of H₂O₂(aq). 2 H₂O₂(aq)→ 2 H₂O(l)+ O₂(g) What is the order of this reaction?

Accepted Answer

The half-life of a first-order reaction is independent of initial concentration. Therefore, the fact that the half-life of this reaction is independent of the concentration of H₂O₂(aq) suggests that this reaction follows first-order kinetics.

Question 8

Acetaldehyde decomposes at 750 K: CH₃CHO → CO + CH₄.The reaction is first order in acetaldehyde and the half-life of the reaction is found to be 530 seconds.What is the rate constant for the reaction at this temperature?

Accepted Answer

The answer of Acetaldehyde decomposes at 750 K: CH₃CHO →...

Question 9

If a sample of ²³³Pa takes 62.7 days to decrease to 20.0% of its original mass,what is its half-life?

Accepted Answer

The answer of If a sample of ²³³Pa takes 62.7...

Question 10

The decay constant,k,is given for each of the beta emitters below.Which one has the shortest half life?

Accepted Answer

The half-life is inversely proportional to the decay constant. The larger the decay constant, the shorter the half-life. ⁴²K has the largest decay constant (1.55 × 10^-5 s^-1), indicating it has the shortest half-life.

Question 11

The decomposition of cyclopropane,was observed at 500°C and its concentration was monitored as a function of time.The data set is given below.What is the order of the reaction with respect to cyclopropane?

Accepted Answer

The answer of The decomposition of cyclopropane,was observed at 500°C...

Question 12

The first-order reaction,SO₂Cl₂ → SO₂ + Cl₂,has a rate constant equal to 2.20 × 10^-5 s^-1 at 593 K.What percentage of the initial amount of SO₂Cl₂ will remain after 2.00 hours?

Accepted Answer

The first-order reaction follows the equation: ln ([SO₂Cl₂]/[SO₂Cl₂]0) = -kt Where [SO₂Cl₂]0 is the initial concentration of SO₂Cl₂ and k is the rate constant. We can rearrange the equation to find the remaining concentration of SO₂Cl₂ after a certain time t: [SO₂Cl₂]/[SO₂Cl₂]0 = e^(-kt) Plugging in the given values: [SO₂Cl₂]/[SO₂Cl₂]0 = e^(-(2.20x10^-5 s^-1)(2.00 hours x 3600 s/hour)) [SO₂Cl₂]/[SO₂Cl₂]0 = 0.146 The percentage remaining can be found by multiplying by 100%: Percentage remaining = 0.146 x 100% = 14.6% ≈ 14.7% Therefore, the best choice is D) 85.4% of the initial amount of SO₂Cl₂ will remain after 2.00 hours.

Question 13

Fluorine-18 is an isotope used in Positron Emission Tomography (PET)to scan the brain.If a researcher has 1.50 μg of ¹⁸F,how long before it decays to 1.0 ng? The half-life of ¹⁸F is 109.8 minutes.

Accepted Answer

The answer of Fluorine-18 is an isotope used in Positron...

Question 14

What percentage of a radioactive substance remains after 6.00 half-lives have elapsed?

Accepted Answer

After each half-life, the amount of radioactive substance remaining is halved. After 6 half-lives, the amount remaining is halved six times, or reduced to 1/2^6 (or 1/64) of the original amount, which is about 1.56%. Therefore, the answer is B, 1.56%.

Question 15

The rate constant,k,for a first-order reaction is equal to 4.2 × 10^-4 s^-1.What is the half-life for the reaction?

Accepted Answer

The half-life, t1/2, of a first-order reaction is given by the equation:
t1/2 = ln2/k
Substituting the given value of k, we get:
t1/2 = ln2/(4.2 × 10^-14 s^-1)
t1/2 = 1.7 × 10^13 s or 17,000,000,000,000 s
This is closest to option C, which is 1.7 × 10^13 s (rounded to two significant figures).

Question 16

For the first-order reaction,2 N₂O(g)→ 2 N₂(g)+ O₂(g),what is the concentration of N₂O after 3 half-lives if 0.15 mol of N₂O is initially placed into in a 1.00-L reaction vessel?

Accepted Answer

First, we need to determine the number of half-lives that have occurred in 3 half-lives. Since a half-life is the time required for the concentration of the reactant to decrease by half, after 1 half-life the concentration is 0.5 times the initial concentration, after 2 half-lives the concentration is 0.25 times the initial concentration, and after 3 half-lives the concentration is 0.125 times the initial concentration.

Using the given initial concentration of 0.15 mol/L, we can calculate the concentration after 3 half-lives:

Final concentration = 0.15 mol/L x (0.5)^3 = 0.01171875 mol/L

This is equivalent to 1.9 x 10^-2 M, which matches answer choice B.

Question 17

For a particular first-order reaction,it takes 48 minutes for the concentration of the reactant to decrease to 25% of its initial value.What is the value for rate constant (in s^-1)for the reaction?

Accepted Answer

The answer of For a particular first-order reaction,it takes 48...

Question 18

Neptunium-239 has a half-life of 2.35 days.How many days must elapse for a sample of ²³⁹Np to decay to 1.00% of its original quantity?

Accepted Answer

To find the number of days required for a sample to decay to 1.00% of its original quantity, we use the formula for exponential decay, which involves the half-life of the substance. The formula to calculate the time for a substance to decay to a certain percentage of its original amount is:$$ t = \left( \frac{\log(\text{final amount} / \text{initial amount})}{\log(0.5)} \right) \times \text{half-life} $$For a substance to decay to 1.00% of its original amount, the final amount/initial amount ratio is 0.01. Given that the half-life of Neptunium-239 is 2.35 days, we substitute these values into the formula:$$ t = \left( \frac{\log(0.01)}{\log(0.5)} \right) \times 2.35 $$This calculation will give the total time required for the sample to decay to 1% of its original quantity. Without doing the exact calculation here, we know from the nature of logarithmic functions and the half-life principle that the time required for such a significant decay (to 1% of the original quantity) would be multiple half-lives, making option D (15.6 days) the correct choice. This is because each half-life reduces the quantity by half, and to reach 1% (or 0.01 of the original), several half-lives are necessary.

Question 19

The following reaction is first order: C₂H₆ → 2 CH₃.If the rate constant is equal to 5.5 × 10^-4 s^-1 at 1000 K,how long will it take for 0.35 mol of C₂H₆ in a 1.00 L container to decrease to 0.10 mol in the same container?

Accepted Answer

The answer of The following reaction is first order: C₂H₆...

Question 20

The first-order reaction,2 N₂O(g)→ 2 N₂(g)+ O₂(g),has a rate constant equal to 0.76 s^-1 at 1000 K.How long will it take for the concentration of N₂O to decrease to 42% of its initial concentration?

Accepted Answer

The integrated rate law for a first-order reaction is:

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

where [A]t is the concentration of A at time t, [A]0 is the initial concentration of A, k is the rate constant, and t is the time.

We are given the rate constant k = 0.76 s^-1 and we want to find the time it takes for [A]t/[A]0 = 0.42.

Substituting the given values into the integrated rate law, we get:

ln(0.42) = -0.76t

Solving for t, we get:

t = ln(0.42)/(-0.76)

t ≈ 1.1 s

Therefore, the answer is choice B.

Quiz 12: Chemical Kinetics

What is the decay constant for a radioactive isotope which decreases to 34% of its original value in 2.48 hours?

An experiment with ⁵⁵Co takes 47.5 hours.At the end of the experiment,1.90 ng of ⁵⁵Co remains.If the half life is 18.0 hours,how many ng of ⁵⁵Co were originally present?

Fluorine-18 is a radioisotope widely used in positron emission tomography to investigate brain activity.The half-life is 109.8 minutes.How long will it take for 2.75 μg of ¹⁸F to decay to 500 ng?

Iodine-123,used in thyroid therapy,has a half-life of 13.27 hours.How many half-lives are required for a 160 mg sample of iodine-123 to decay to 5.0 mg?

The first-order reaction,SO₂Cl₂ → SO₂ + Cl₂,has a half-life of 8.75 hours at 593 K.How long will it take for the concentration of SO₂Cl₂ to fall to 12.5% of its initial value?

The isomerization reaction,CH₃NC → CH₃CN,is first order and the rate constant is equal to 0) 46 s^-1 at 600 K.What is the concentration of CH₃NC after 0.20 minutes if the initial concentration is 0.10 M?

The half life of the reaction shown below is found not to depend on the concentration of H₂O₂(aq) . 2 H₂O₂(aq) → 2 H₂O(l) + O₂(g) What is the order of this reaction?

Acetaldehyde decomposes at 750 K: CH₃CHO → CO + CH₄.The reaction is first order in acetaldehyde and the half-life of the reaction is found to be 530 seconds.What is the rate constant for the reaction at this temperature?

If a sample of ²³³Pa takes 62.7 days to decrease to 20.0% of its original mass,what is its half-life?

The decay constant,k,is given for each of the beta emitters below.Which one has the shortest half life?

The decomposition of cyclopropane,was observed at 500°C and its concentration was monitored as a function of time.The data set is given below.What is the order of the reaction with respect to cyclopropane?

The first-order reaction,SO₂Cl₂ → SO₂ + Cl₂,has a rate constant equal to 2.20 × 10^-5 s^-1 at 593 K.What percentage of the initial amount of SO₂Cl₂ will remain after 2.00 hours?

Fluorine-18 is an isotope used in Positron Emission Tomography (PET) to scan the brain.If a researcher has 1.50 μg of ¹⁸F,how long before it decays to 1.0 ng? The half-life of ¹⁸F is 109.8 minutes.

What percentage of a radioactive substance remains after 6.00 half-lives have elapsed?

The rate constant,k,for a first-order reaction is equal to 4.2 × 10^-4 s^-1.What is the half-life for the reaction?

For the first-order reaction,2 N₂O(g) → 2 N₂(g) + O₂(g) ,what is the concentration of N₂O after 3 half-lives if 0.15 mol of N₂O is initially placed into in a 1.00-L reaction vessel?

For a particular first-order reaction,it takes 48 minutes for the concentration of the reactant to decrease to 25% of its initial value.What is the value for rate constant (in s^-1) for the reaction?

Neptunium-239 has a half-life of 2.35 days.How many days must elapse for a sample of ²³⁹Np to decay to 1.00% of its original quantity?

The following reaction is first order: C₂H₆ → 2 CH₃.If the rate constant is equal to 5.5 × 10^-4 s^-1 at 1000 K,how long will it take for 0.35 mol of C₂H₆ in a 1.00 L container to decrease to 0.10 mol in the same container?

The first-order reaction,2 N₂O(g) → 2 N₂(g) + O₂(g) ,has a rate constant equal to 0.76 s^-1 at 1000 K.How long will it take for the concentration of N₂O to decrease to 42% of its initial concentration?

Quiz 12: Chemical Kinetics

What is the decay constant for a radioactive isotope which decreases to 34% of its original value in 2.48 hours?

An experiment with 55Co takes 47.5 hours.At the end of the experiment,1.90 ng of 55Co remains.If the half life is 18.0 hours,how many ng of 55Co were originally present?

Fluorine-18 is a radioisotope widely used in positron emission tomography to investigate brain activity.The half-life is 109.8 minutes.How long will it take for 2.75 μg of 18F to decay to 500 ng?

Iodine-123,used in thyroid therapy,has a half-life of 13.27 hours.How many half-lives are required for a 160 mg sample of iodine-123 to decay to 5.0 mg?

The first-order reaction,SO2Cl2 → SO2 + Cl2,has a half-life of 8.75 hours at 593 K.How long will it take for the concentration of SO2Cl2 to fall to 12.5% of its initial value?

The isomerization reaction,CH3NC → CH3CN,is first order and the rate constant is equal to 0) 46 s-1 at 600 K.What is the concentration of CH3NC after 0.20 minutes if the initial concentration is 0.10 M?

The half life of the reaction shown below is found not to depend on the concentration of H2O2(aq) . 2 H2O2(aq) → 2 H2O(l) + O2(g) What is the order of this reaction?

Acetaldehyde decomposes at 750 K: CH3CHO → CO + CH4.The reaction is first order in acetaldehyde and the half-life of the reaction is found to be 530 seconds.What is the rate constant for the reaction at this temperature?

If a sample of 233Pa takes 62.7 days to decrease to 20.0% of its original mass,what is its half-life?

The decay constant,k,is given for each of the beta emitters below.Which one has the shortest half life?

The decomposition of cyclopropane,was observed at 500°C and its concentration was monitored as a function of time.The data set is given below.What is the order of the reaction with respect to cyclopropane?

The first-order reaction,SO2Cl2 → SO2 + Cl2,has a rate constant equal to 2.20 × 10-5 s-1 at 593 K.What percentage of the initial amount of SO2Cl2 will remain after 2.00 hours?

Fluorine-18 is an isotope used in Positron Emission Tomography (PET) to scan the brain.If a researcher has 1.50 μg of 18F,how long before it decays to 1.0 ng? The half-life of 18F is 109.8 minutes.

What percentage of a radioactive substance remains after 6.00 half-lives have elapsed?

The rate constant,k,for a first-order reaction is equal to 4.2 × 10-4 s-1.What is the half-life for the reaction?

For the first-order reaction,2 N2O(g) → 2 N2(g) + O2(g) ,what is the concentration of N2O after 3 half-lives if 0.15 mol of N2O is initially placed into in a 1.00-L reaction vessel?

For a particular first-order reaction,it takes 48 minutes for the concentration of the reactant to decrease to 25% of its initial value.What is the value for rate constant (in s-1) for the reaction?

Neptunium-239 has a half-life of 2.35 days.How many days must elapse for a sample of 239Np to decay to 1.00% of its original quantity?

The following reaction is first order: C2H6 → 2 CH3.If the rate constant is equal to 5.5 × 10-4 s-1 at 1000 K,how long will it take for 0.35 mol of C2H6 in a 1.00 L container to decrease to 0.10 mol in the same container?

The first-order reaction,2 N2O(g) → 2 N2(g) + O2(g) ,has a rate constant equal to 0.76 s-1 at 1000 K.How long will it take for the concentration of N2O to decrease to 42% of its initial concentration?

An experiment with ⁵⁵Co takes 47.5 hours.At the end of the experiment,1.90 ng of ⁵⁵Co remains.If the half life is 18.0 hours,how many ng of ⁵⁵Co were originally present?

Fluorine-18 is a radioisotope widely used in positron emission tomography to investigate brain activity.The half-life is 109.8 minutes.How long will it take for 2.75 μg of ¹⁸F to decay to 500 ng?

The first-order reaction,SO₂Cl₂ → SO₂ + Cl₂,has a half-life of 8.75 hours at 593 K.How long will it take for the concentration of SO₂Cl₂ to fall to 12.5% of its initial value?

The isomerization reaction,CH₃NC → CH₃CN,is first order and the rate constant is equal to 0) 46 s^-1 at 600 K.What is the concentration of CH₃NC after 0.20 minutes if the initial concentration is 0.10 M?

The half life of the reaction shown below is found not to depend on the concentration of H₂O₂(aq) . 2 H₂O₂(aq) → 2 H₂O(l) + O₂(g) What is the order of this reaction?

Acetaldehyde decomposes at 750 K: CH₃CHO → CO + CH₄.The reaction is first order in acetaldehyde and the half-life of the reaction is found to be 530 seconds.What is the rate constant for the reaction at this temperature?

If a sample of ²³³Pa takes 62.7 days to decrease to 20.0% of its original mass,what is its half-life?

The first-order reaction,SO₂Cl₂ → SO₂ + Cl₂,has a rate constant equal to 2.20 × 10^-5 s^-1 at 593 K.What percentage of the initial amount of SO₂Cl₂ will remain after 2.00 hours?

Fluorine-18 is an isotope used in Positron Emission Tomography (PET) to scan the brain.If a researcher has 1.50 μg of ¹⁸F,how long before it decays to 1.0 ng? The half-life of ¹⁸F is 109.8 minutes.

The rate constant,k,for a first-order reaction is equal to 4.2 × 10^-4 s^-1.What is the half-life for the reaction?

For the first-order reaction,2 N₂O(g) → 2 N₂(g) + O₂(g) ,what is the concentration of N₂O after 3 half-lives if 0.15 mol of N₂O is initially placed into in a 1.00-L reaction vessel?

For a particular first-order reaction,it takes 48 minutes for the concentration of the reactant to decrease to 25% of its initial value.What is the value for rate constant (in s^-1) for the reaction?

Neptunium-239 has a half-life of 2.35 days.How many days must elapse for a sample of ²³⁹Np to decay to 1.00% of its original quantity?

The following reaction is first order: C₂H₆ → 2 CH₃.If the rate constant is equal to 5.5 × 10^-4 s^-1 at 1000 K,how long will it take for 0.35 mol of C₂H₆ in a 1.00 L container to decrease to 0.10 mol in the same container?

The first-order reaction,2 N₂O(g) → 2 N₂(g) + O₂(g) ,has a rate constant equal to 0.76 s^-1 at 1000 K.How long will it take for the concentration of N₂O to decrease to 42% of its initial concentration?