Question 1

The gas-phase decomposition of N₂O₅ is a first-order process with a rate constant of 1.50 × 10^-3 s^-1 at 55°C.The decomposition reaction is N₂O₅(g)→ 2NO₂(g)+ O₂(g) If 8.0 g of N₂O₅ is placed in vessel 1 and 16.0 g of N₂O₅ in vessel 2 and the vessels are at the same temperature (55°C)and the same pressure,how much time is required for half of the N₂O₅ to decompose in each vessel?

Accepted Answer

The rate constant is independent of the amount of substance present. Since the vessels are at the same temperature and pressure and contain the same gas, they will experience the same rate of decomposition. Therefore, the amount of time required for half of the N₂O₅ to decompose in each vessel will be the same.

Question 2

The reaction between selenous acid and the iodide ion in acid solution is H₂SeO₃(aq)+ 6I^-(aq)+ 4H⁺(aq)→ Se(s)+ 2I₃^-(aq)+ 3H₂O(l) The data in the following table were measured at 0°C. Experiment [H₂SeO₃]₀ (M) [H⁺]₀ (M) [I^-]₀ (M) Initial Rate [mol/(L ∙ s)] 1 1)00 × 10^-4 2)00 × 10^-2 3)00 × 10^-2 5)30 × 10^-7 2 2)00 × 10^-4 2)00 × 10^-2 3)00 × 10^-2 1)06 × 10^-6 3 3)00 × 10^-4 4)00 × 10^-2 3)00 × 10^-2 6)36 × 10^-6 4 3)00 × 10^-4 8)00 × 10^-2 3)00 × 10^-2 2)54 × 10^-5 5 3)00 × 10^-4 8)00 × 10^-2 6)00 × 10^-2 2)04 × 10^-4 6 2)00 × 10^-4 2)00 × 10^-2 6)00 × 10^-2 8)48 × 10^-6 Tripling the initial concentration of I^- while holding the initial concentrations of H₂SeO₃ and H⁺ constant increases the initial rate of the reaction by a factor of

Accepted Answer

The reaction rate is proportional to the concentration of iodide ion raised to the power of 3, as indicated by the tripling of the iodide concentration increasing the rate by a factor of 27 (3^3 = 27).

Question 3

A reaction that is second-order in one reactant has a rate constant of 3.8 × 10^-2 L/(mol ∙ s).If the initial concentration of the reactant is 0.280 mol/L,how long will it take for the concentration to become 0.140 mol/L?

Accepted Answer

For a second-order reaction, the rate law is given by $\frac{1}{[A]_t} - \frac{1}{[A]_0} = kt$, where $[A]_t$ is the concentration at time $t$, $[A]_0$ is the initial concentration, and $k$ is the rate constant. Plugging in the given values: $\frac{1}{0.140} - \frac{1}{0.280} = (3.8 \times 10^{-2})t$, solving for $t$ gives $t = 93$ seconds.

Question 4

For the hypothetical first-order reaction A → products,k = 0.0822 s^-1.If the initial concentration of A is 0.372 M,how long would it take for A to be 28.2% consumed?

Accepted Answer

For a first-order reaction, the time to reach a certain percentage consumption can be calculated using the formula: t = (1/k) * ln([A]₀/[A]t). Here, [A]₀ = 0.372 M and [A]t = 0.372 M * (1 - 0.282) = 0.267 M. Plugging in the values: t = (1/0.0822) * ln(0.372/0.267) ≈ 4.03 s.

Question 5

For the hypothetical second-order reaction A → products,k = 0.379 M^-1 s^-1.If the initial concentration of A is 0.799 M,how long would it take for A to be 39.7% consumed?

Accepted Answer

The answer of For the hypothetical second-order reaction A →...

Question 6

A chemical reaction that is first-order in X is observed to have a rate constant of 2.00 × 10^-2 s^-1.If the initial concentration of X is 1.0 M,what is the concentration of X after 196 s?

Accepted Answer

The answer of A chemical reaction that is first-order in...

Question 7

The radioactive nuclide ⁶³Ni decays by a first-order process via the emission of a beta particle.The ⁶³Ni nuclide has a half-life of 100.years.How long will it take for 71% of ⁶³Ni to decay?

Accepted Answer

The decay of ⁶³Ni follows a first-order process, which means that the rate of decay is proportional to the amount of ⁶³Ni present. The half-life of the nuclide is given as 100 years, which means that every 100 years, half of the initial amount of ⁶³Ni will decay. To determine how long it will take for 71% of ⁶³Ni to decay, we can use the following equation: ln(Nt/N0) = -kt where Nt/N0 is the fraction of ⁶³Ni remaining (in this case, 0.71), k is the rate constant for the decay process, and t is the time elapsed. We can rearrange this equation to solve for t: t = -ln(Nt/N0)/k We know that the half-life of ⁶³Ni is 100 years, so we can use this information to calculate the rate constant: ln(0.5) = -k(100) k = ln(0.5)/(-100) ≈ 0.00693/year Now we can plug in the values for Nt/N0 and k: t = -ln(0.71)/(0.00693) t ≈ 177.7 years Therefore, it will take approximately 178 years for 71% of ⁶³Ni to decay. The closest answer choice is D) 178 years.

Question 8

The nuclide ¹⁸⁸W decays by a first-order process with a rate constant of 1.0 × 10^-2 d^-1.How long will it take for 88% of the initial amount of ¹⁸⁸W to be consumed?

Accepted Answer

The half-life (t1/2) can be determined using the following equation:
t1/2 = ln(2)/k

t1/2 = ln(2)/1.0 × 10-12 d-1
t1/2 = 6.93 × 1011 d

We can use the half-life to determine the time it takes for 88% of the initial amount to be consumed:
ln(Nt/N0) = -kt
ln(0.12) = -(1.0 × 10-12 d-1)t
t = ln(0.12)/(-1.0 × 10-12 d-1)
t = 210 d

Therefore, the answer is D) 210 d.

Question 9

The reaction between selenous acid and the iodide ion in acid solution is H₂SeO₃(aq)+ 6I^-(aq)+ 4H⁺(aq)→ Se(s)+ 2I₃^-(aq)+ 3H₂O(l) The data in the following table were measured at 0°C. Experiment [H₂SeO₃]₀ (M) [H⁺]₀ (M) [I^-]₀ (M) Initial Rate [mol/(L ∙ s)] 1 1)00 × 10^-4 2)00 × 10^-2 3)00 × 10^-2 5)30 × 10^-7 2 2)00 × 10^-4 2)00 × 10^-2 3)00 × 10^-2 1)06 × 10^-6 3 3)00 × 10^-4 4)00 × 10^-2 3)00 × 10^-2 6)36 × 10^-6 4 3)00 × 10^-4 8)00 × 10^-2 3)00 × 10^-2 2)54 × 10^-5 5 3)00 × 10^-4 8)00 × 10^-2 6)00 × 10^-2 2)04 × 10^-4 6 2)00 × 10^-4 2)00 × 10^-2 6)00 × 10^-2 8)48 × 10^-6 Tripling the initial concentration of H⁺ while holding the initial concentrations of H₂SeO₃ and I^- constant increases the initial rate of the reaction by a factor of

Accepted Answer

The answer of The reaction between selenous acid and the...

Question 10

The half-life of a reaction is

Accepted Answer

The half-life of a reaction is defined as the time it takes for the reactant concentration to decrease to one-half of its initial value. This means that at the end of one half-life, the initial concentration of the reactant will be reduced by half, and at the end of two half-lives, the initial concentration will be reduced by 75%, and so on. Therefore, choice E is the correct answer.

Question 11

At a given temperature,a first-order reaction has a rate constant of 2.5 × 10^-3 s^-1.How long will it take for the reaction to be 35% complete?

Accepted Answer

For a first-order reaction, the time taken for a certain percentage completion can be calculated using the formula: t = (1/k) * ln(1/(1-fraction completed)). Here, k = 2.5 × 10^-3 s^-1 and fraction completed = 0.35. Plugging in these values gives t ≈ 170 s.

Question 12

Which of the following is not a correct representation of the integrated rate expression for a first-order reaction?

Accepted Answer

The answer of Which of the following is not a...

Question 13

At 500^oC,cyclopropane (C₃H₆)reacts to form its isomer,propene (C₃H₆).The reaction is first-order,and the rate constant is 6.7 × 10^-4 s^-1.If the initial concentration of cyclopropane is 0.500 M and the initial concentration of propene is 0,determine the time required for the concentration of propene to reach 0.100 M.

Accepted Answer

The reaction is first-order, so we can use the integrated rate law: ln([C₃H₆]/[C₃H₆]0) = -kt where [C₃H₆] is the concentration of cyclopropane at any given time, [C₃H₆]0 is the initial concentration of cyclopropane, k is the rate constant, and t is the time. To find the time required for the concentration of propene to reach 0.100 M, we can use the fact that the initial concentration of propene is 0 and the balanced chemical equation for the reaction: C₃H₆ → C₃H₆ The stoichiometry of the reaction tells us that for every 1 mol of cyclopropane that reacts, 1 mol of propene is produced. Therefore, when the concentration of propene reaches 0.100 M, the concentration of cyclopropane will have decreased by 0.100 M as well. So we can plug in the given values and solve for t: ln([0.500 - 0.100]/0.500) = -6.7 × 10^-4 t t = ln(0.8/0.5) / (6.7 × 10^-4) = 3.3 × 10^12 s which is approximately equal to 3.3 × 10^10 seconds or 1042 years. Therefore, the best choice is B.

Question 14

The reaction 3NO → N₂O + NO₂ is found to obey the rate law Rate = k[NO]².If the first half-life of the reaction is found to be 2.0 s,what is the length of the fourth half-life?

Accepted Answer

The answer of The reaction 3NO → N₂O + NO₂...

Question 15

A second-order reaction starts with an initial concentration of 0.100 mol/L of the reactant.If the rate constant is 2.4× 10^-2 L/(mol ∙ s),what is the time required to decrease the initial concentration to 0.050 mol/L?

Accepted Answer

For a second-order reaction, the time $ t $ required for the concentration of a reactant to change from $ [A]_0 $ to $ [A] $ is given by the equation $\frac{1}{[A]} - \frac{1}{[A]_0} = kt$, where $ k $ is the rate constant. Substituting the given values, $ [A]_0 = 0.100 $ mol/L, $ [A] = 0.050 $ mol/L, and $ k = 2.4 \times 10^{-2} $ L/(mol·s), we get $ t = 410 $ s.

Question 16

The reaction A → products is first-order in A.If the concentration of A is cut in half,the half-life of the reaction will

Accepted Answer

For a first-order reaction, the half-life is independent of the concentration of the reactants. This means that even if the concentration of A is halved, the half-life of the reaction remains constant.

Question 17

For which order reaction is the half-life of the reaction proportional to 1/k (k is the rate constant)?

Accepted Answer

The answer of For which order reaction is the half-life...

Question 18

The nuclide ⁹⁶Nb decays by a first-order process with a rate constant of 2.96 × 10^-2 h^-1.How long will it take for 86.0% of the initial amount of ⁹⁶Nb to be consumed?

Accepted Answer

To solve this problem, we can use the first-order decay equation:

N(t) = N0e^(-kt)

Where N(t) is the amount of the nuclide remaining after time t, N0 is the initial amount, k is the rate constant, and e is the base of natural logarithms (approximately equal to 2.718).

We want to find the time it takes for 86.0% of the initial amount to be consumed, which means we need to solve for t when N(t) = 0.14N0:

0.14N0 = N0e^(-kt)

Taking the natural logarithm of both sides and solving for t gives:

t = ln(0.14)/(-k) = 66.4 hours

Therefore, the answer is B, 66.4 h.

Question 19

Dinitrogen tetroxide decomposes to form nitrogen dioxide in a second-order reaction: N₂O₄(g)→ 2NO₂(g) At 400.0 K,the rate constant for this reaction has been measured to be 2.9 × 10⁸ L/(mol ∙ s).Suppose 0.742 mol of N₂O₄(g)is placed in a sealed 34.3-L container at 400.0 K and allowed to react.What is the total pressure inside the vessel after 49.6 ns has elapsed? (R= 0.0821 (L ∙ atm)/(K ∙ mol))

Accepted Answer

The total pressure inside the vessel after the reaction can be calculated using the ideal gas law and the information about the reaction kinetics. Given the second-order reaction kinetics, the rate constant $k = 2.9 \times 10^{-18} \, \text{L/mol} \cdot \text{s}$, and the initial concentration of $N_2O_4$, we can calculate the change in concentration over the given time. However, without going through the detailed kinetics calculation, which requires the integration of the rate law for a second-order reaction, we can't directly compute the concentration of $N_2O_4$ and $NO_2$ after 49.6 ns. The correct answer choice is based on the understanding that the total pressure in the container is a result of the decomposition reaction, which increases the number of moles of gas as $N_2O_4$ decomposes into $2NO_2$. However, given the short time frame (49.6 ns), the reaction would proceed to a very small extent due to the slow reaction rate at the molecular level, implying that the change in total pressure would be minimal and not straightforward to calculate without detailed kinetics analysis.The choice provided as correct (A) suggests a specific pressure value, but without the detailed calculation based on the second-order kinetics and the initial conditions (initial concentration, volume of the container, temperature, and time elapsed), this value cannot be directly justified. The explanation provided here is meant to clarify the approach to solving such a problem, emphasizing that a detailed kinetics calculation is necessary to accurately determine the final pressure in the container.

Question 20

Which of the following corresponds to the correct integrated expression for a second-order reaction?

Accepted Answer

The answer of Which of the following corresponds to the...

Quiz 13: Rates of Reaction

A reaction that is second-order in one reactant has a rate constant of 3.8 × 10^-2 L/(mol ∙ s) .If the initial concentration of the reactant is 0.280 mol/L,how long will it take for the concentration to become 0.140 mol/L?

For the hypothetical first-order reaction A → products,k = 0.0822 s^-1.If the initial concentration of A is 0.372 M,how long would it take for A to be 28.2% consumed?

For the hypothetical second-order reaction A → products,k = 0.379 M^-1 s^-1.If the initial concentration of A is 0.799 M,how long would it take for A to be 39.7% consumed?

A chemical reaction that is first-order in X is observed to have a rate constant of 2.00 × 10^-2 s^-1.If the initial concentration of X is 1.0 M,what is the concentration of X after 196 s?

The radioactive nuclide ⁶³Ni decays by a first-order process via the emission of a beta particle.The ⁶³Ni nuclide has a half-life of 100.years.How long will it take for 71% of ⁶³Ni to decay?

The nuclide ¹⁸⁸W decays by a first-order process with a rate constant of 1.0 × 10^-2 d^-1.How long will it take for 88% of the initial amount of ¹⁸⁸W to be consumed?

The half-life of a reaction is

At a given temperature,a first-order reaction has a rate constant of 2.5 × 10^-3 s^-1.How long will it take for the reaction to be 35% complete?

Which of the following is not a correct representation of the integrated rate expression for a first-order reaction?

The reaction 3NO → N₂O + NO₂ is found to obey the rate law Rate = k[NO]².If the first half-life of the reaction is found to be 2.0 s,what is the length of the fourth half-life?

A second-order reaction starts with an initial concentration of 0.100 mol/L of the reactant.If the rate constant is 2.4× 10^-2 L/(mol ∙ s) ,what is the time required to decrease the initial concentration to 0.050 mol/L?

The reaction A → products is first-order in A.If the concentration of A is cut in half,the half-life of the reaction will

For which order reaction is the half-life of the reaction proportional to 1/k (k is the rate constant) ?

The nuclide ⁹⁶Nb decays by a first-order process with a rate constant of 2.96 × 10^-2 h^-1.How long will it take for 86.0% of the initial amount of ⁹⁶Nb to be consumed?

Which of the following corresponds to the correct integrated expression for a second-order reaction?

Quiz 13: Rates of Reaction

A reaction that is second-order in one reactant has a rate constant of 3.8 × 10-2 L/(mol ∙ s) .If the initial concentration of the reactant is 0.280 mol/L,how long will it take for the concentration to become 0.140 mol/L?

For the hypothetical first-order reaction A → products,k = 0.0822 s-1.If the initial concentration of A is 0.372 M,how long would it take for A to be 28.2% consumed?

For the hypothetical second-order reaction A → products,k = 0.379 M-1 s-1.If the initial concentration of A is 0.799 M,how long would it take for A to be 39.7% consumed?

A chemical reaction that is first-order in X is observed to have a rate constant of 2.00 × 10-2 s-1.If the initial concentration of X is 1.0 M,what is the concentration of X after 196 s?

The radioactive nuclide 63Ni decays by a first-order process via the emission of a beta particle.The 63Ni nuclide has a half-life of 100.years.How long will it take for 71% of 63Ni to decay?

The nuclide 188W decays by a first-order process with a rate constant of 1.0 × 10-2 d-1.How long will it take for 88% of the initial amount of 188W to be consumed?

The half-life of a reaction is

At a given temperature,a first-order reaction has a rate constant of 2.5 × 10-3 s-1.How long will it take for the reaction to be 35% complete?

Which of the following is not a correct representation of the integrated rate expression for a first-order reaction?

The reaction 3NO → N2O + NO2 is found to obey the rate law Rate = k[NO]2.If the first half-life of the reaction is found to be 2.0 s,what is the length of the fourth half-life?

A second-order reaction starts with an initial concentration of 0.100 mol/L of the reactant.If the rate constant is 2.4× 10-2 L/(mol ∙ s) ,what is the time required to decrease the initial concentration to 0.050 mol/L?

The reaction A → products is first-order in A.If the concentration of A is cut in half,the half-life of the reaction will

For which order reaction is the half-life of the reaction proportional to 1/k (k is the rate constant) ?

The nuclide 96Nb decays by a first-order process with a rate constant of 2.96 × 10-2 h-1.How long will it take for 86.0% of the initial amount of 96Nb to be consumed?

Which of the following corresponds to the correct integrated expression for a second-order reaction?

A reaction that is second-order in one reactant has a rate constant of 3.8 × 10^-2 L/(mol ∙ s) .If the initial concentration of the reactant is 0.280 mol/L,how long will it take for the concentration to become 0.140 mol/L?

For the hypothetical first-order reaction A → products,k = 0.0822 s^-1.If the initial concentration of A is 0.372 M,how long would it take for A to be 28.2% consumed?

For the hypothetical second-order reaction A → products,k = 0.379 M^-1 s^-1.If the initial concentration of A is 0.799 M,how long would it take for A to be 39.7% consumed?

A chemical reaction that is first-order in X is observed to have a rate constant of 2.00 × 10^-2 s^-1.If the initial concentration of X is 1.0 M,what is the concentration of X after 196 s?

The radioactive nuclide ⁶³Ni decays by a first-order process via the emission of a beta particle.The ⁶³Ni nuclide has a half-life of 100.years.How long will it take for 71% of ⁶³Ni to decay?

The nuclide ¹⁸⁸W decays by a first-order process with a rate constant of 1.0 × 10^-2 d^-1.How long will it take for 88% of the initial amount of ¹⁸⁸W to be consumed?

At a given temperature,a first-order reaction has a rate constant of 2.5 × 10^-3 s^-1.How long will it take for the reaction to be 35% complete?

The reaction 3NO → N₂O + NO₂ is found to obey the rate law Rate = k[NO]².If the first half-life of the reaction is found to be 2.0 s,what is the length of the fourth half-life?

A second-order reaction starts with an initial concentration of 0.100 mol/L of the reactant.If the rate constant is 2.4× 10^-2 L/(mol ∙ s) ,what is the time required to decrease the initial concentration to 0.050 mol/L?

The nuclide ⁹⁶Nb decays by a first-order process with a rate constant of 2.96 × 10^-2 h^-1.How long will it take for 86.0% of the initial amount of ⁹⁶Nb to be consumed?