Question

Radon- 220 is radioactive, and decays into polonium- 216 . This is a first-order process, just like the radioactive decay of carbon-14, and it has a rate constant of $0.0125 \mathrm{~s}^{-1}$. When the concentration of radon-220 is $1.0 \times 10^{-9} \mathrm{~mol}$ $\mathrm{L}^{-1}$, what is the rate of the reaction?

Name: Problem 59, Chapter 14: Chemistry The Molecular Nature of Matter
Uploaded: 2022-01-10T20:57:36-08:00
Duration: 1 min 1 s
Channel: Crystal Wang
Description: Radon- 220 is radioactive, and decays into polonium- 216 . This is a first-order process, just like the radioactive decay of carbon-14, and it has a rate constant of 0.0125 s^-1. When the concentration of radon-220 is 1.0 ×10^-9 mol L^-1, what is the rate of the reaction?

   Radon- 220 is radioactive, and decays into polonium- 216 . This is a first-order process, just like the radioactive decay of carbon-14, and it has a rate constant of $0.0125 \mathrm{~s}^{-1}$. When the concentration of radon-220 is $1.0 \times 10^{-9} \mathrm{~mol}$ $\mathrm{L}^{-1}$, what is the rate of the reaction?

Chemistry The Molecular Nature of Matter

Neil D. Jespersen,… 6th Edition

Chapter 14, Problem 59

Instant Answer

Solved by Expert Crystal Wang

01/10/2022

Step 1

Step 1: The rate of a first-order reaction is given by the formula: \[rate = k[A]\] where $k$ is the rate constant and \([A]\] is the concentration of the reactant. Show more…

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Radon- 220 is radioactive, and decays into polonium- 216 . This is a first-order process, just like the radioactive decay of carbon-14, and it has a rate constant of $0.0125 \mathrm{~s}^{-1}$. When the concentration of radon-220 is $1.0 \times 10^{-9} \mathrm{~mol}$ $\mathrm{L}^{-1}$, what is the rate of the reaction?

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Key Concepts

First-Order Kinetics

In a first-order reaction, the reaction rate is directly proportional to the concentration of one reactant. This means that the rate at which the reactant transforms is given by the rate constant multiplied by its concentration, leading to an exponential decrease in concentration over time.

Rate Constant

The rate constant is a proportionality factor in the rate law that defines the speed of a reaction. For first-order reactions, it has units of inverse time (e.g., s?¹) and directly influences how quickly a reactant is consumed.

Rate Law

The rate law is a mathematical expression that relates the rate of a reaction to the concentrations of the reactants and the rate constant. In a first-order process, the rate law takes the simple form Rate = k [A], where k is the rate constant and [A] is the concentration of the reactant.

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