   # Hydrogen iodide decomposes when heated, forming H 2 (g) and I 2 (g). The rate law for this reaction is –Δ[HI]/Δ t = k [HI] 2 . At 443°C, k = 30. L/mol · min. If the initial HI(g) concentration is 1.5 × 10 −2 mol/L, what concentration of HI(g) will remain after 10. minutes? ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

#### Solutions

Chapter
Section ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 14, Problem 24PS
Textbook Problem
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## Hydrogen iodide decomposes when heated, forming H2(g) and I2(g). The rate law for this reaction is –Δ[HI]/Δt = k[HI]2. At 443°C, k = 30. L/mol · min. If the initial HI(g) concentration is 1.5 × 10−2 mol/L, what concentration of HI(g) will remain after 10. minutes?

Interpretation Introduction

Interpretation: The concentration remains after 10 mins has to be given.

Concept Introduction:

Integrated rate law for second order reactions:

Taking in the example of following reaction,

aAproducts

And the reaction follows second order rate law,

Then the relationship between the concentration of A and time can be mathematically expressed as,

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

The above expression is called as integrated rate for second order reactions.

### Explanation of Solution

The concentration remains after 10 mins is calculated as,

-Δ[R]Δt = k[R]2,The relation can be transformed into,1[R]t - 1[R]0 = ktGiven:Initialconcentration,[HI]0  = 1.5×10-2 mol/LFinalconcentration,[HI]t = ?k = 30mol/L.st = 10 minsTherefore,1[R]t - 1[R]0 = kt1

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