Textbook Question
(b) How can you calculate the rate constant for a first-order reaction from the graph you made in part (a)?
Ch.14 - Chemical Kinetics
Chapter 14, Problem 41b
(b) At 320°C the rate constant is 2.2 × 10-5 s-1. What is the half-life at this temperature?
Recommended similar problem, with video answer:
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
1mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Rate Constant
The rate constant (k) is a proportionality factor in the rate equation of a chemical reaction, indicating the speed of the reaction at a given temperature. It is specific to the reaction and varies with temperature, reflecting how the frequency of effective collisions between reactants changes. In this case, the rate constant is given as 2.2 × 10<sup>-5</sup> s<sup>-1</sup>, which is essential for calculating the half-life.
Recommended video:
Guided course
00:45
Rate Constant Units
Half-Life
Half-life is the time required for the concentration of a reactant to decrease to half of its initial value. For first-order reactions, the half-life is inversely proportional to the rate constant, allowing for straightforward calculations. The formula for half-life (t<sub>1/2</sub>) in first-order kinetics is t<sub>1/2</sub> = 0.693/k, where k is the rate constant.
Recommended video:
Guided course
02:17Zero-Order Half-life
First-Order Kinetics
First-order kinetics describes a reaction where the rate is directly proportional to the concentration of one reactant. This means that as the concentration decreases, the rate of reaction also decreases. The relationship between the rate constant and half-life in first-order reactions simplifies calculations, making it easier to determine how long it takes for a substance to reduce to half its amount.
Recommended video:
Guided course
02:29First-Order Reactions
Related Practice
Textbook Question
The decomposition of sodium bicarbonate (baking soda), NaHCO3(s), into Na2CO3(s), H2O(l), and CO2(g) at constant pressure requires the addition of 85 kJ of heat per two moles of NaHCO3. (b) Draw an enthalpy diagram for the reaction.
1260
views
Textbook Question
(a) The gas-phase decomposition of SO2Cl2, SO2Cl2(g) → SO2(g) + Cl2(g), is first order in SO2Cl2. At 600 K the half-life for this process is 2.3 × 105 s. What is the rate constant at this temperature?
1430
views
Open Question
Molecular iodine, I2(g), dissociates into iodine atoms at 625 K with a first-order rate constant of 0.271 s-1. (b) If you start with 0.050 M I2 at this temperature, how much will remain after 5.12 s assuming that the iodine atoms do not recombine to form I2?
Textbook Question
As described in Exercise 14.41, the decomposition of sulfuryl chloride (SO2Cl2) is a first-order process. The rate constant for the decomposition at 660 K is 4.5 × 10-2 s-1. (a) If we begin with an initial SO2Cl2 pressure of 450 torr, what is the partial pressure of this substance after 60 s?
Textbook Question
As described in Exercise 14.41, the decomposition of sulfuryl chloride (SO2Cl2) is a first-order process. The rate constant for the decomposition at 660 K is 4.5 × 10-2 s-1. (b) At what time will the partial pressure of SO2Cl2 decline to one-tenth its initial value?
1755
views