   Chapter 20, Problem 107IP

Chapter
Section
Textbook Problem

# lndium(III) phosphide is a semiconducting material that has been frequently used in lasers, light-emitting diodes (LED), and fiber-optic devices. This material can be synthesized at 900. K according to the following reaction: ln ( CH 3 ) 3 ( g ) + PH 3 ( g ) → lnP ( s ) + 3CH 4 ( g ) a. If 2.56 L In(CH3)3 at 2.00 atm is allowed to react with 1.38 L PH3 at 3.00 atm, what mass of InP(s) will be produced assuming the reaction has an 87% yield?b. When an electric current is passed through an optoelectronic device containing InP, the light emitted has an energy of 2.03 × 10−19 J. What is the wavelength of this light and is it visible to the human eye?c. The semiconducting properties of InP can be altered by doping. If a small number of phosphorus atoms are replaced by atoms with an electron configuration of [Kr]5s24d105p4, is this n-type or p-type doping?

(a)

Interpretation Introduction

Interpretation: The reaction between In(CH3)3 and PH3 at 900K is given. The answers are to be stated for the given options.

Concept introduction: The number of moles is calculated using ideal gas law,

PV=nRTn=PVRT

To determine: The mass of InP when 2.56L In(CH3)3 at 2.00atm is allowed to react with 1.38L PH3 at 3.00atm (assuming the reaction has 87% yield).

Explanation

Explanation

Given

Temperature is 900K .

Pressure of In(CH3)3 is 2.00atm .

Volume of In(CH3)3 is 2.56L .

Pressure of PH3 is 3.00atm .

Volume of PH3 is 1.38L .

Formula

Number of moles is calculated as,

PV=nRTn=PVRT (1)

Where,

• P is the total pressure.
• V is the volume.
• n is the total moles.
• R is the universal gas constant (0.08206Latm/Kmol) .
• T is the absolute temperature.

Substitute the values of P,V,R and T for PH3 in the above equation.

nPH3=PVRT=2.00atm×1.38L(0.08206Latm/Kmol)(900K)=0.056mol_

Substitute the values of P,V,R and T for In(CH3)3 in equation (1).

nIn(CH3)3=PVRT=2.00atm×2.56L(0.08206Latm/Kmol)(900K)=0.0693mol_

To determine the mass of InP is 7

(b)

Interpretation Introduction

Interpretation: The reaction between In(CH3)3 and PH3 at 900K is given. The answers are to be stated for the given options.

Concept introduction: The number of moles is calculated using ideal gas law,

PV=nRTn=PVRT

To determine: The wavelength of light if 2.03×1019J of energy is emitted by light; if this wavelength is visible to human eye.

(c)

Interpretation Introduction

Interpretation: The reaction between In(CH3)3 and PH3 at 900K is given. The answers are to be stated for the given options.

Concept introduction: The number of moles is calculated using ideal gas law,

PV=nRTn=PVRT

To determine: If InP becomes n-type or p-type when small number of phosphorous atoms are replaced by the atoms of electronic configuration [Kr]5s24d105p4 .

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