   # The decomposition of phosphine, PH 3 , proceeds according to the equation PH 3 (g) → 1 4 P 4 (g) + 3 2 H 2 (g) It is found that the reaction has the following rate equation: Rate = k [PH 3 ]. The half-life of PH 3 is 37.9 seconds at 120 °C. (a) How much time is required for three fourths of the PH 3 to decompose? (b) What fraction of the original sample of PH 3 remains after 1.00 minute? ### 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 64GQ
Textbook Problem
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## The decomposition of phosphine, PH3, proceeds according to the equation PH 3 (g) → 1 4  P 4 (g) + 3 2  H 2 (g) It is found that the reaction has the following rate equation: Rate = k[PH3]. The half-life of PH3 is 37.9 seconds at 120 °C. (a) How much time is required for three fourths of the PH3 to decompose? (b) What fraction of the original sample of PH3 remains after 1.00 minute?

(a)

Interpretation Introduction

Interpretation:

The time required to decompose phosphine about three fourths of its original value should be determined.

The fraction of the original sample of phosphine remains after 1.00 minute should be determined.

Concept introduction:

Rate law or rate equation: 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.

aA + bBxXRate of reaction = k [A]m[B]n

Order of a reaction:  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.

Rate constant, k: 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.

### Explanation of Solution

The given reaction is a first order reaction since the rate equation determines it and its rate equation is as follows,

k=2.303tlog[A0][A]Where,[A0]= initialconcentrationk=rate constantt=time[A]=concentrationaftertimet

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(b)

Interpretation Introduction

Interpretation:

The time required to decompose phosphine about three fourths of its original value should be determined.

The fraction of the original sample of phosphine remains after 1.00 minute should be determined.

Concept introduction:

Rate law or rate equation: 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.

aA + bBxXRate of reaction = k [A]m[B]n

Order of a reaction:  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.

Rate constant, k: 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.

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