   # Hypofluorous acid, HOF, is very unstable, decomposing in a first-order reaction to give HF and O 2 , with a half-life of 30. minutes at room temperature: HOF(g) → HF(g) + ½ O 2 (g) If the partial pressure of HOF in a 1.00-L flask is initially 1.00 × 10 2 mm Hg at 25 °C, what are the total pressure in the flask and the partial pressure of HOF after exactly 30 minutes? After 45 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 77GQ
Textbook Problem
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## Hypofluorous acid, HOF, is very unstable, decomposing in a first-order reaction to give HF and O2, with a half-life of 30. minutes at room temperature:HOF(g) → HF(g) + ½ O2(g)If the partial pressure of HOF in a 1.00-L flask is initially 1.00 × 102 mm Hg at 25 °C, what are the total pressure in the flask and the partial pressure of HOF after exactly 30 minutes? After 45 minutes?

Interpretation Introduction

Interpretation:

For the given reaction under given conditions the total pressure and partial pressure of HOF gas after 30 minutes and after 45 minute should be determined.

Concept introduction:

In order to establish the plausibility of a mechanism, one must compare the rate law of the rate determining step to the experimentally determined rate law.

Rate determining step: In a chemical reaction the rate determining step is the slowest step in which the rate of the reaction depends on the rate of that slowest step.

Rate law: It is generally the rate equation that consists of the reaction rate with the concentration or the pressures of the reactants and constant parameters.

Rate constant: The rate constant for a chemical reaction is the proportionality term in the chemical reaction rate law which gives the relationship between the rate and the concentration of the reactant present in the chemical reaction.

Rate order: The order of each reactant in a reaction is represented by the exponential term of the respective reactant present in the rate law and the overall order of the reaction is the sum of all the exponents of all reactants present in the chemical reaction.  The order of the reaction is directly proportional to the concentration of the reactants.

Half-lifet1/2: The half-life period is defined as the time required by the reactant to reduce its concentration to one half of its initial concentration.

Activation energy: It is defined as the minimum energy required by the reacting species in order to undergo chemical reaction.

Intermediate species: It is the species formed during the middle of the chemical reaction between the reactant and the desired product.

### Explanation of Solution

Given:

Partial pressure of HOF = 1×102mmHgTemperature=25oCTotal pressure after 30 minutes = ?Total pressure after 45 minutes = ?Half life = 30 minutesVolume = 1L

In order to find the total pressure first the rate constant value should be calculated which is determined as follows,

t1/2=0.693kk=0.693t1/2=0.69330 m=0.0231min1

Now, the pressure for the given gas after 30 minutes is calculated as follows,

k=2.303tlogP0P0.0231min1=2.30330log100mmHgPlog100mmHgP=30×0.0231min12.303log100mmHgP=0.3100mmHgP=100

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