Indium(III) phosphide is a semiconducting material that has...

Indium(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 $900 . \mathrm{K}$ according to the following reaction: $$ \operatorname{In}\left(\mathrm{CH}_{3}\right)_{3}(g)+\mathrm{PH}_{3}(g) \longrightarrow \operatorname{InP}(s)+3 \mathrm{CH}_{4}(g) $$ a. If $2.56 \mathrm{~L}$ of $\mathrm{In}\left(\mathrm{CH}_{3}\right)_{3}$ at $2.00 \mathrm{~atm}$ is allowed to react with $1.38 \mathrm{~L}$ of $\mathrm{PH}_{3}$ at $3.00 \mathrm{~atm}$, what mass of $\operatorname{In} \mathrm{P}(s)$ will be produced assuming the reaction is $87 \%$ efficient? b. When an electric current is passed through an optoelectronic device containing $\mathrm{InP}$, the light emitted has an energy of $2.03 \times 10^{-19} \mathrm{~J}$. 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 $[\mathrm{Kr}] 5 s^{2} 4 d^{10} 5 p^{4}$, is this n-type or p-type doping?

Indium(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 $900 . \mathrm{K}$ according to the following reaction:
$$
\operatorname{In}\left(\mathrm{CH}_{3}\right)_{3}(g)+\mathrm{PH}_{3}(g) \longrightarrow \operatorname{InP}(s)+3 \mathrm{CH}_{4}(g)
$$
a. If $2.56 \mathrm{~L}$ of $\mathrm{In}\left(\mathrm{CH}_{3}\right)_{3}$ at $2.00 \mathrm{~atm}$ is allowed to react with $1.38 \mathrm{~L}$ of $\mathrm{PH}_{3}$ at $3.00 \mathrm{~atm}$, what mass of $\operatorname{In} \mathrm{P}(s)$ will be produced assuming the reaction is $87 \%$ efficient?
b. When an electric current is passed through an optoelectronic device containing $\mathrm{InP}$, the light emitted has an energy of $2.03 \times 10^{-19} \mathrm{~J}$. 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 $[\mathrm{Kr}] 5 s^{2} 4 d^{10} 5 p^{4}$, is this n-type or p-type doping?

Key Concepts

Photon Energy-Wavelength Relationship

The relationship between the energy of a photon and its wavelength is defined by the equation E = hc/?, where h is Planck’s constant and c is the speed of light. This concept is fundamental in physical chemistry and quantum mechanics for understanding how light of different wavelengths corresponds to specific energies.

Semiconductor Doping

Semiconductor doping involves intentionally introducing impurities into an intrinsic semiconductor to alter its electrical properties, either by adding extra electrons (n-type) or creating holes (p-type). The type and behavior of the dopant are determined by its electron configuration relative to the atoms it replaces, which influences the conductivity and performance of semiconductor devices.

Ideal Gas Law

The Ideal Gas Law (PV = nRT) relates the pressure, volume, temperature, and number of moles of a gas. This relationship is used to determine the quantity of gaseous reactants or products under specified conditions, making it an essential tool in stoichiometric calculations for reactions involving gases.

Visible Light Spectrum

The visible light spectrum refers to the range of wavelengths that the human eye is capable of detecting, typically between 400 and 700 nanometers. Understanding this range is important in applications involving optoelectronic devices, where the emission of light in the visible range determines the device’s practical usability.

Limiting Reactant

The concept of a limiting reactant is central in determining how much product can be formed in a chemical reaction. When reactants are not present in the exact stoichiometric proportions required by the balanced equation, the reactant that is completely consumed first limits the overall amount of product that can be generated.

Reaction Stoichiometry

Reaction stoichiometry involves using the balanced chemical equation to understand the quantitative relationships between reactants and products. It allows one to convert between moles (or volumes, under certain conditions) of compounds, ensuring that each component participates according to the mole ratios dictated by the balanced reaction.

Percent Yield

Percent yield compares the actual amount of product obtained from a reaction to the theoretical maximum predicted by stoichiometry. It is a measure of reaction efficiency and accounts for practical losses and incomplete reactions that often occur in laboratory and industrial processes.