CHEM: INTEGRATED RATE LAWS & ARRHENIUS EQUATION STUDY MODULE

A substance, A, decomposes according to zero-order kinetics with a rate constant, k = 3.80 × 10−2 M∙s−1, that decays for 24.5 seconds from its initial concentration of 1.25 M. What is the final concentration of A?

0.319 M [A]t = -kt + [A]0 [A]t = -(3.80×10-2 M·s-1)(24.5 s) + 1.25 M [A]t = 0.319 M

By what factor does the rate constant increase when the temperature increases from 200. K to 400. K for a reaction with an activation energy of 845 J/mol?

1.3 ln k2/k1 = 845/8.314 (1/200 - 1/400) ln k2/k1 = 0.254 k2/k1 = 1.3

What is the activation energy for a reaction when the rate constant doubles when the temperature increase from 150. K to 450. K?

1.30 × 10^3 J/mol ln 2 = (Ea/ 8.314) ((1/150) - (1/450)) Ea = 1.30 x10^3 J/ mol

What is the activation energy for a reaction when the rate constant increases by a factor of 3.5 when the temperature increase from 125 K to 625 K?

1.63 × 10^3 J/mol ln 3.5 = Ea/ 8.314 (1/125 - 1/625) Ea = 1.63 x 10^3 J/mol

A substance, A, decomposes according to zero-order kinetics from an initial concentration of 1.90 M to 0.420 M in 85.2 seconds. What is the value of rate constant, k?

1.74 × 10−2 M∙s−1

Which plot represents a second-order reaction?

1/[A] on the left side of graph & Time (t) on the bottom

Which equation shows the integrated rate law for a substance that reacts according to second-order kinetics?

1/[A]t = kt + 1/[A]0

A substance reacts with zero-order kinetics and its concentration goes from 1.30 M to 0.89 M in 12 minutes. What is its half-life?

19 min [A]t = -kt + [A]0 0.89 M = -k(12 min) + 1.30 M k = 3.4 × 10-2 M·min-1 t(1/2) = [1.30M]o / 2(3.4 x 10^-2) t(1/2) = 19 min

HI decomposes into its elements according to second-order kinetics. How long will it take for the concentration to decrease to 1.25 M from an initial concentration of 2.25 M? The rate constant, k, equals 1.6 × 10−3 M−1hr−1. 2 HI(g) → H2(g) + I2(g)

2.2 × 10^2 hours 1/[1.25]t = (1.6x10^-3)t + 1/[2.25M]o 0.356 = (1.6x10^-3)t t= 2.2x10^2 hr

HI decomposes into its elements according to second-order kinetics. What concentration of HI remains from an initial concentration of 2.30 M after 4.5 hours? The rate constant, k, equals 1.6 × 10−3 M−1s−1. 2 HI(g) → H2(g) + I2(g)

2.26 M 1/[A]t = (1.6 x10^-3)(4.5hr) + 1/[2.30M]0 1/[A]t = 0.442 [A]t = 2.26 M

A reaction follows zero-order kinetics and decays to half of its original concentration of 2.50 M in 53 seconds. What is the value of the rate constant, k?

2.4 × 10−2 M−1∙s−1 [A]t = -kt + [A]0 1.25 M = -k(53 s) + 2.50 M k = 2.4 × 10-2 M·s-1

N2O5 decomposes to form NO2 and O2 with first-order kinetics. The initial concentration of N2O5 is 3.0 M and the reaction runs for 3.5 minutes. If the rate constant, k, equals 5.89 × 10−3, what is the final concentration of N2O5?

2.9 M

The rate constant for the decomposition of N2O5 is 7.78 × 10−7 at 273 K and 3.46 × 10−5 at T2. If the activation energy is 1027 kJ/mol, what is the final temperature? 2 N2O5(g) → 4 NO2(g) + O2(g)

275 K

Radioactive decay follows first-order kinetics. If sodium-24 has a half-life of 14.96 hours, what is its rate constant, k?

4.63 × 10^−2 hr−1

The reaction of NO and O3 reacts with second order kinetics. If it takes 94 seconds for the concentration of NO to go from 3.00 M to 1.25 M, what is the rate constant, k? NO(g) + O3(g) → NO2(g) + O2(g)

4.96 × 10-3 M−1∙s−1

N2O5 decomposes to form NO2 and O2 with first-order kinetics. How long does it take for the N2O5 concentration to decrease from its initial value of 2.75 M to its final value of 1.85 M, if the rate constant, k, equals 5.89 × 10−3?

67.3 minutes ln[A]t = -kt + ln[A]0 ln[1.85]t = -(5.89×10-3 min-1)t + ln[2.75 M]0 t = 67.3 min

A substance, Z, with an initial concentration of 1.75 M follows second-order kinetics and decays with a half-life of 6.8 minutes. What is the value of the rate constant, k?

8.4 × 10−2 M−1∙min−1 6.8 min = 1 / k[1.75M]0 K = 8.4 × 10−2 M−1∙min−1

The rate constant for the decomposition of HI is 3.45 × 10−3 at 325 K. What is the rate constant, k2, at 425 K given an activation energy of 592 kJ/mol?

8.44 × 10^19 lnk2 - ln(3.45e-3) = (5.92e5/ 8.314)(1/325 - 1/425) lnK2= 45.88 k2 = 8.44 x 10^19

Radioactive decay follows first-order kinetics. If a sample of I-131 decays from 25.0 mg to 8.25 mg in 12.8 days, what is the rate constant, k?

8.66 × 10−2 day−1

A substance, A, decays according to zero-order kinetics with a rate constant, k = 4.94 × 10−2 M∙s−1. How long does it take for a 0.750 M sample decay to 0.315 M?

8.81 seconds [A]t = -kt + [A]0 0.315 M = -(4.94×10-2 M·s-1)(t) + 0.750 M t = 8.81 s

Which best defines half-life?

Half-life is the time it takes for the amount of a substance to decrease to half of its original value.

What are the units for the rate constant, k, for a zero-order reaction?

M·s−1

What are the units for the rate constant, k, for a second-order reaction?

M−1∙s−1

Which plot represents a zero-order reaction?

[A] on the left side of graph & Time(t) on the bottom of graph

Which equation represents the integrated rate law for a zero-order reaction?

[A]t = -kt + [A]0

Which plot represents a first-order reaction?

ln[A] on the left side of the graph & Time (t) on the bottom of graph

Which equation shows the integrated rate law for a substance that reacts according to first-order kinetics?

ln[A]t = -kt + ln[A]0

What are the units for the rate constant, k, for a first-order reaction?

s−1

Identify the half-life equation for substances that follow first-order kinetics.

t(1/2) = 0.693/k

Identify the half-life equation for substances that follow second-order kinetics.

t(1/2) = 1/ k[A]0