Question 1

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 0.20 mol in the same container?

Accepted Answer

For a first-order reaction, the time can be calculated using the formula: t = (1/k) * ln([A]₀/[A]). Substituting the given values: k = 5.5 × 10⁻⁴ s⁻¹, [A]₀ = 0.35 mol/L, [A] = 0.20 mol/L, we find t ≈ 1020 seconds, which is approximately 17 minutes.

Question 2

For a particular first-order reaction,it takes 24 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 first-order rate law is given by:

Rate = k[A]

where [A] is the concentration of the reactant and k is the rate constant.

From the problem, we know that:

[A]t = 0.25[A]0

where [A]t is the concentration of the reactant at time t and [A]0 is the initial concentration of the reactant.

We can use the integrated rate law for a first-order reaction to solve for the rate constant:

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

Taking natural logarithms of both sides:

ln(0.25) = -k(24 min)

Solving for k:

k = ln(0.25) / (-24 min) = 9.6 × 10^-4 min^-1

Since the answer choices are given in units of s^-1, we need to convert the rate constant:

k = 9.6 × 10^-4 min^-1 x 60 s/min = 5.8 × 10^-5 s^-1

Therefore, the best choice is B.

Question 3

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 6.00 hours?

Accepted Answer

For a first-order reaction, the remaining concentration can be calculated using the formula: [A] = [A]₀e^(-kt). Converting 6 hours to seconds (6 × 3600 = 21600 s) and substituting the given values, the percentage remaining is approximately 62.2%.

Question 4

Carbon-14,which is present in all living tissue,radioactively decays via a first-order process.A one-gram sample of wood taken from a living tree gives a rate for carbon-14 decay of 13.6 counts per minute.If the half-life for carbon-14 is 5720 years,how old is a wood sample that gives a rate for carbon-14 decay of 11.9 counts per minute?

Accepted Answer

The age of the wood sample can be calculated using the first-order decay equation: ln(N0/N) = kt, where N0 is the initial rate (13.6 counts/min), N is the current rate (11.9 counts/min), k is the decay constant (calculated from the half-life), and t is the time. Solving for t gives approximately 1.1 × 10^3 years.

Question 5

Nitrogen dioxide decomposes at 300 °C via a second-order process to produce nitrogen monoxide and oxygen according to the following chemical equation: 2 NO₂(g)→ 2 NO(g)+ O₂(g). A sample of NO₂(g)is initially placed in a 2.50 L reaction vessel at 300 °C.If the half-life and the rate constant at 300 °C are 11 seconds and 0.54 L mol^-1 s^-1,respectively,how many moles of NO₂ were in the original sample?

Accepted Answer

The second-order rate law can be written as follows:

Rate = k[N2O4]^2

Using half-life equation for a second-order reaction:

t1/2 = 1 / k[N2O4]

Plugging in the given values:

11 s = 1 / (0.54 L mol^-1 s^-1)[N2O4]

[N2O4] = 0.42 mol L^-1

To find the total moles of N2O4 in the original sample:

moles = concentration × volume = 0.42 mol L^-1 × 2.50 L = 1.05 mol

Therefore, the answer is B) 0.42 mol.

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 0.30 mol L^-1?

Accepted Answer

The integrated rate law for a first-order reaction is:ln[A]t = -kt + ln[A]0where [A]t is the concentration of the reactant at time t, k is the rate constant, and [A]0 is the initial concentration of the reactant.Substituting the given values into the integrated rate law, we get:ln[CH3NC]t = -0.46 s-1 * 0.20 min * 60 s/min + ln(0.30 mol L-1)ln[CH3NC]t = -5.52 + ln(0.30 mol L-1)[CH3NC]t = 1.2 × 10-3 mol L-1

Question 7

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 16.5% of its initial value?

Accepted Answer

For a first-order reaction, the time $ t $ required for the concentration of a reactant to fall to a fraction $ f $ of its initial value is given by the formula $ t = \frac{\ln(1/f)}{k} $, where $ k $ is the rate constant. The half-life ($ t_{1/2} $) of a first-order reaction is related to the rate constant by $ t_{1/2} = \frac{\ln(2)}{k} $. Given that the half-life is 8.75 hours, we can find $ k $ and then calculate $ t $ for the concentration to fall to 16.5% (or 0.165) of its initial value.1. Calculate the rate constant $ k $ using the half-life formula:$$ k = \frac{\ln(2)}{t_{1/2}} = \frac{\ln(2)}{8.75} $$2. Calculate the time $ t $ for the concentration to fall to 16.5% of its initial value:$$ t = \frac{\ln(1/0.165)}{k} = \frac{\ln(1/0.165)}{\ln(2)/8.75} $$This calculation will give $ t $ as approximately 22.7 hours, which means it takes 22.7 hours for the concentration to fall to 16.5% of its initial value.

Question 8

Decomposes in the gas phase by the reaction 
The reaction is first order in   And the rate constant is 3.0 ×   At 600 K.A vessel is charged with 2.4 atm of  At 600 K.The partial pressure of   At  Is ________ atm.

Accepted Answer

We can use the following equation to find the partial pressure of A at time t:

P_A = P_total (1 - e^(-kt))

Where P_total is the total pressure, k is the rate constant, and t is the time.

Since we are interested in the partial pressure of A at equilibrium, we can set t equal to infinity and simplify the equation to:

P_A = P_total

So the partial pressure of A at equilibrium is equal to the initial partial pressure of A, which is 2.4 atm.

To find the partial pressure of B at equilibrium, we can use the same equation and substitute in the appropriate values:

P_B = P_total (1 - e^(-kt))
P_B = (2.4 atm) (1 - e^(-(3.0 × 10^11 s^-1) (600 K^-1) t))
P_B = (2.4 atm) (1 - e^(-1.8 × 10^8 s^-1))

Solving for P_B gives:

P_B = 0.98 atm

Therefore, the answer is C.

Question 9

The isomerization of methylisonitrile to acetonitrile NC(g)→ CN(g) Is first order in NC.The half-life of the reaction is 5.20 × 10¹ s at 545 K.The rate constant when the initial [ NC] is 0.030 mol L^-1 is ________ .

Accepted Answer

The half-life of the reaction is given by:

t1/2 = ln2 / k

where k is the rate constant.

Substituting the given half-life and solving for k:

5.20 × 10^1 s = ln2 / k

k = ln2 / (5.20 × 10^1 s)

k = 0.0133 s^-1

The rate law is first order in [NC], therefore:

rate = k[NC]

Substituting the given initial concentration and rate constant:

rate = (0.0133 s^-1)(0.030 mol L^-1) = 3.99 x 10^-4 mol L^-1 s^-1

Therefore, the answer is (C) 0.0133.

Question 10

The decomposition of   In solution in carbon tetrachloride proceeds via the reaction

The reaction is first order and has a rate constant of 4.82 ×   
At 64 °C.If the reaction is initiated with 0.058 mol in a 1.00 L vessel,how many moles remain after 151 s?

Accepted Answer

The answer of The decomposition of   In solution...

Question 11

The reaction that occurs in a Breathalyzer,a device used to determine the alcohol level in a person's bloodstream,is given below.If the rate of appearance of Cr₂(SO₄)₃ is 1.64 mol min^-1 at a particular moment,what is the rate of disappearance of C₂H₆O at that moment? 2 K₂Cr₂O₇(aq)+ 8 H₂SO₄(aq)+ 3 C₂H₆O(aq)→ 2 Cr₂(SO₄)₃(aq)+ 2 K₂SO₄(aq)+ 11 H₂O(l)

Accepted Answer

The answer of The reaction that occurs in a Breathalyzer,a...

Question 12

The second-order reaction 2 Mn(CO)₅ → Mn₂(CO)₁₀ has a rate constant equal to 3.0 × 10⁹ L mol^-1 s^-1 at 25 °C.If the initial concentration of Mn(CO)₅ is 2.0 × 10^-5 mol L^-1,how long will it take for 90.% of the reactant to disappear?

Accepted Answer

The rate law for the reaction is:

Rate = k[Mn(CO)S1U1B15S1U1B0]S1U1P2[S1U1B0]S1U1P1

where k = 3.0 × 10S1U1P19S1S1P0 L molS1U1P1-1S1S1P0 sS1U1P1-1S1S1P0.

The half-life for a second-order reaction is:

tS1U1P1/2S1S1P0 = 1 / k[Mn(CO)S1U1B15S1U1B0]S1U1P1

We can use this equation to find the time it takes for 90% of the reactant to disappear:

ln ([Mn(CO)S1U1B15S1U1B0]S1U1P1 / [Mn(CO)S1U1B15S1U1B0]S1U1B0]) = -kt

0.9[Mn(CO)S1U1B15S1U1B0]S1U1B0 = [Mn(CO)S1U1B15S1U1B0]S1U1P1(1 - 0.1)

[Mn(CO)S1U1B15S1U1B0]S1U1B0 / [Mn(CO)S1U1B15S1U1B0]S1U1P1 = 9

ln 9 = - k t

t = ln 9 / k

t = ln 9 / (3.0 × 10S1U1P19S1S1P0 L molS1U1P1-1S1S1P0 sS1U1P1-1S1S1P0 × 2.0 × 10S1U1P1-5S1S1P0 mol LS1U1P1-1S1S1P0) = 1.5 × 10S1U1P1-S1S1P0S1U1P14S1S1P0 s

Therefore, the best choice is C.

Question 13

The elementary reaction (g)→ 2 NO(g)+ (g) Is second order in And the rate constant at 501 K is 7.93 × 10^-3 .The reaction half-life at this temperature when = 0.45 mol L^-1 is ________ s.

Accepted Answer

The answer of The elementary reaction  (g)→ 2 NO(g)+...

Question 14

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

Accepted Answer

The answer of For the first-order reaction,2 N₂O(g)→ 2 N₂(g)+...

Question 15

In aqueous solution,hypobromite ion,BrO^-,reacts to produce bromate ion,BrO₃^-,and bromide ion,Br^-,according to the following chemical equation: A plot of 1/[BrO^-] vs.time is linear and the slope is equal to 0.056 L mol^-1s^-1.If the initial concentration of BrO^- is 0.80 mol L^-1,how long will it take one-half of the BrO^-ion to react?

Accepted Answer

The answer of In aqueous solution,hypobromite ion,BrO^-,reacts to produce bromate...

Question 16

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 formula for calculating the half-life of a first-order reaction is:

t1/2 = (ln 2)/k

where k is the rate constant.

Plugging in the given value of k, we get:

t1/2 = (ln 2)/4.2 × 10-14 s-1

Using a calculator, we get:

t1/2 = 1.67 × 10^13 s

This can be expressed in scientific notation as:

t1/2 = 1.7 × 10^13 s

Therefore, the best choice is C: 1.7 × 10^13 s.

Question 17

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 12% of its initial concentration?

Accepted Answer

For a first-order reaction, the time to reach a certain concentration is given by the formula t = (1/k) * ln([A]₀/[A]). Here, [A]₀/[A] = 1/0.12, k = 0.76 s⁻¹. Plugging in the values, t = (1/0.76) * ln(1/0.12) ≈ 2.8 s.

Question 18

The isomerization of methylisonitrile to acetonitrile NC(g)→ CN(g) Is first order in NC.The rate constant for the reaction is 9.45 × 10^-5 At 478 K.The Of the reaction when the initial [ NC] is 0.030 mol L^-1 is ________ s.

Accepted Answer

The answer of The isomerization of methylisonitrile to acetonitrile 
...

Question 19

The combustion of ethylene proceeds by the reaction (g)+ (g)→ (g)+ O(g) When the rate of disappearance of Is 0.28 mol L^-1 ,the rate of appearance of Is ________

Accepted Answer

The answer of The combustion of ethylene proceeds by the...

Question 20

The combustion of ethylene proceeds by the reaction (g)+ 3 (g)→ 2 C (g)+ O(g) When the rate of disappearance of Is 0.23 mol L^-1 ,the rate of disappearance of Is ________

Accepted Answer

The answer of The combustion of ethylene proceeds by the...

Quiz 20: Chemical Kinetics

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 0.20 mol in the same container?

For a particular first-order reaction,it takes 24 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?

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 6.00 hours?

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 0.30 mol L^-1?

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 16.5% of its initial value?

Decomposes in the gas phase by the reaction The reaction is first order in And the rate constant is 3.0 × At 600 K.A vessel is charged with 2.4 atm of At 600 K.The partial pressure of At Is ________ atm.

The isomerization of methylisonitrile to acetonitrile NC(g) → CN(g) Is first order in NC.The half-life of the reaction is 5.20 × 10¹ s at 545 K.The rate constant when the initial [ NC] is 0.030 mol L^-1 is ________ .

The decomposition of In solution in carbon tetrachloride proceeds via the reaction The reaction is first order and has a rate constant of 4.82 × At 64 °C.If the reaction is initiated with 0.058 mol in a 1.00 L vessel,how many moles remain after 151 s?

The second-order reaction 2 Mn(CO) ₅ → Mn₂(CO) ₁₀ has a rate constant equal to 3.0 × 10⁹ L mol^-1 s^-1 at 25 °C.If the initial concentration of Mn(CO) ₅ is 2.0 × 10^-5 mol L^-1,how long will it take for 90.% of the reactant to disappear?

The elementary reaction (g) → 2 NO(g) + (g) Is second order in And the rate constant at 501 K is 7.93 × 10^-3 .The reaction half-life at this temperature when = 0.45 mol L^-1 is ________ s.

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

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?

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 12% of its initial concentration?

The isomerization of methylisonitrile to acetonitrile NC(g) → CN(g) Is first order in NC.The rate constant for the reaction is 9.45 × 10^-5 At 478 K.The Of the reaction when the initial [ NC] is 0.030 mol L^-1 is ________ s.

The combustion of ethylene proceeds by the reaction (g) + (g) → (g) + O(g) When the rate of disappearance of Is 0.28 mol L^-1 ,the rate of appearance of Is ________

The combustion of ethylene proceeds by the reaction (g) + 3 (g) → 2 C (g) + O(g) When the rate of disappearance of Is 0.23 mol L^-1 ,the rate of disappearance of Is ________

Quiz 20: Chemical Kinetics

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 0.20 mol in the same container?

For a particular first-order reaction,it takes 24 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?

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 6.00 hours?

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 0.30 mol L-1?

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 16.5% of its initial value?

Decomposes in the gas phase by the reaction The reaction is first order in And the rate constant is 3.0 × At 600 K.A vessel is charged with 2.4 atm of At 600 K.The partial pressure of At Is ________ atm.

The isomerization of methylisonitrile to acetonitrile NC(g) → CN(g) Is first order in NC.The half-life of the reaction is 5.20 × 101 s at 545 K.The rate constant when the initial [ NC] is 0.030 mol L-1 is ________ .

The decomposition of In solution in carbon tetrachloride proceeds via the reaction The reaction is first order and has a rate constant of 4.82 × At 64 °C.If the reaction is initiated with 0.058 mol in a 1.00 L vessel,how many moles remain after 151 s?

The second-order reaction 2 Mn(CO) 5 → Mn2(CO) 10 has a rate constant equal to 3.0 × 109 L mol-1 s-1 at 25 °C.If the initial concentration of Mn(CO) 5 is 2.0 × 10-5 mol L-1,how long will it take for 90.% of the reactant to disappear?

The elementary reaction (g) → 2 NO(g) + (g) Is second order in And the rate constant at 501 K is 7.93 × 10-3 .The reaction half-life at this temperature when = 0.45 mol L-1 is ________ s.

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

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?

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 12% of its initial concentration?

The isomerization of methylisonitrile to acetonitrile NC(g) → CN(g) Is first order in NC.The rate constant for the reaction is 9.45 × 10-5 At 478 K.The Of the reaction when the initial [ NC] is 0.030 mol L-1 is ________ s.

The combustion of ethylene proceeds by the reaction (g) + (g) → (g) + O(g) When the rate of disappearance of Is 0.28 mol L-1 ,the rate of appearance of Is ________

The combustion of ethylene proceeds by the reaction (g) + 3 (g) → 2 C (g) + O(g) When the rate of disappearance of Is 0.23 mol L-1 ,the rate of disappearance of Is ________

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 0.20 mol in the same container?

For a particular first-order reaction,it takes 24 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?

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 6.00 hours?

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 0.30 mol L^-1?

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 16.5% of its initial value?

The isomerization of methylisonitrile to acetonitrile NC(g) → CN(g) Is first order in NC.The half-life of the reaction is 5.20 × 10¹ s at 545 K.The rate constant when the initial [ NC] is 0.030 mol L^-1 is ________ .

The second-order reaction 2 Mn(CO) ₅ → Mn₂(CO) ₁₀ has a rate constant equal to 3.0 × 10⁹ L mol^-1 s^-1 at 25 °C.If the initial concentration of Mn(CO) ₅ is 2.0 × 10^-5 mol L^-1,how long will it take for 90.% of the reactant to disappear?

The elementary reaction (g) → 2 NO(g) + (g) Is second order in And the rate constant at 501 K is 7.93 × 10^-3 .The reaction half-life at this temperature when = 0.45 mol L^-1 is ________ s.

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

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?

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 12% of its initial concentration?

The isomerization of methylisonitrile to acetonitrile NC(g) → CN(g) Is first order in NC.The rate constant for the reaction is 9.45 × 10^-5 At 478 K.The Of the reaction when the initial [ NC] is 0.030 mol L^-1 is ________ s.

The combustion of ethylene proceeds by the reaction (g) + (g) → (g) + O(g) When the rate of disappearance of Is 0.28 mol L^-1 ,the rate of appearance of Is ________

The combustion of ethylene proceeds by the reaction (g) + 3 (g) → 2 C (g) + O(g) When the rate of disappearance of Is 0.23 mol L^-1 ,the rate of disappearance of Is ________