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 \(\mathrm{L} \operatorname{In}\left(\mathrm{CH}_{3}\right)_{3}\) at 2.00 \(\mathrm{atm}\) is allowed to react with 1.38 \(\mathrm{L} \mathrm{PH}_{3}\) at \(3.00 \mathrm{atm},\) 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 $2.03 \times 10^{-19} \mathrm{J}$ . 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?

Step by step solution

01

Part a: Calculating the mass of InP produced

Given variables: \(V_{In(CH_3)_3} = 2.56 \, L\) \(P_{In(CH_3)_3} = 2.00 \, atm\) \(V_{PH_3} = 1.38 \, L\) \(P_{PH_3} = 3.00 \, atm\) \(T = 900 \, K\) Reaction yield: \(87\%\) 1. Calculate moles of In(CH\(_3\)\(_3\) and PH\(_3\) using the Ideal Gas Law (\(PV = nRT\)). \( n_{In(CH_3)_3} = \frac{P_{In(CH_3)_3} V_{In(CH_3)_3}}{R T}\) \( n_{PH_3} = \frac{P_{PH_3} V_{PH_3}}{R T}\) 2. Compare the mole ratio to determine the limiting reactant. Observe the stoichiometry of the balanced equation and compare the moles calculated from the given initial quantities. 3. Calculate the moles of InP formed based on the limiting reactant and reaction yield (87%). Multiply the moles of the limiting reactant by the reaction yield and the stoichiometric ratio. 4. Calculate the mass of InP produced. Using the molar mass of InP, convert the moles of InP formed to mass.

02

Part b: Calculating the wavelength of emitted light

Given variables: Energy of the emitted light: \(2.03 \times 10^{-19} \, J\) 1. Use the Planck's equation to find the wavelength of the emitted light. \(E = h f\), and \(f = \frac{c}{\lambda}\), therefore, \(E = \frac{hc}{\lambda}\). 2. Calculate the wavelength in nanometers: Solve for the wavelength, \(\lambda\), and convert it to nanometers. 3. Determine if the wavelength is visible to the human eye. Based on the visible light spectrum (approx 380 nm to 740 nm), decide if the calculated wavelength is visible or not.

03

Part c: Identifying the doping process

Given electron configuration for the doping metal atom: \([Kr] 5s^2 4d^{10} 5p^4\) 1. Identify the group of the doping metal in the periodic table: Analyze the electron configuration provided to determine the doping metal's group number in the periodic table. 2. Compare the number of valence electrons of the doping metal with phosphorus: Compare the valence electron count of the doping metal with that of phosphorus atoms in InP. 3. Determine if it's n-type or p-type doping: Based on the comparison made, identify if the doping results in n-type or p-type semiconducting InP.

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