Chapter 12: Q4. (page 398)

Calculate the half-life, in years, for the reaction $2 X \to Y$ when the starting concentration of $X$ is $6 μM$ and the rate constant is $3.6 \times 10^{‐ 3} M^{‐ 1} s^{‐ 1}$ .

Short Answer

Expert verified

The half-life in years for the reaction $2 X \to Y$ is $1.47$ years.

Step by step solution

Introduction

Thehalf-life period is the time it takes for a substance's concentration to decline to half of its initial value. The half-life of a reaction is unaffected by the reaction's initial concentration.

Calculate the half-life

The initial concentration of $X$ is $6 μM$ .

Rate constant $= 3.6 \times 10^{‐ 3} M^{‐ 1} s^{‐ 1}$

The half-lifeof a bimolecular reaction is

$t_{\frac{1}{2}} = \frac{1}{k [A]} t_{\frac{1}{2}} = \frac{1}{(3.6 \times 10^{‐ 3} M^{‐ 1} s^{‐ 1}) \times (6 \times 10^{‐ 6} M)} = 4.63 \times 10^{9} s$

Calculate the half-life in years

The half-life period in years is

$= 4.63 \times 10^{7} \times \frac{1}{3600} \times \frac{1}{24} \times \frac{1}{365} = 1.47 years$

Thus, the half-life for the reaction of $2 X \to Y$ is $1.47$ years.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Biology Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Calculate the half-life, in years, for the reaction $2 X \to Y$ when the starting concentration of $X$ is $6 μM$ and the rate constant is $3.6 \times 10^{‐ 3} M^{‐ 1} s^{‐ 1}$ .

Short Answer

Step by step solution

Introduction

Calculate the half-life

Calculate the half-life in years

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Biology Textbooks

Genetic Information

Ecology

Substance Exchange

Organ Systems

Biological Organisms

Microbiology

Study anywhere. Anytime. Across all devices.

Calculate the half-life, in years, for the reaction2X→Y when the starting concentration of X is6μM and the rate constant is 3.6×10‐3M‐1s‐1.

Short Answer

Step by step solution

Introduction

Calculate the half-life

Calculate the half-life in years

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Biology Textbooks

Genetic Information

Ecology

Substance Exchange

Organ Systems

Biological Organisms

Microbiology

Study anywhere. Anytime. Across all devices.

Calculate the half-life, in years, for the reaction $2 X \to Y$ when the starting concentration of $X$ is $6 μM$ and the rate constant is $3.6 \times 10^{‐ 3} M^{‐ 1} s^{‐ 1}$ .