Questions: Problem 1 (25 pts) USE ELEMENT BALANCES TO SOLVE. One of the most common commercial methods for the production of pure silicon that is to be used for the manufacture of semiconductors is the Siemens process of chemical vapor deposition (CVD). A chamber contains a heated silicon rod and a mixture of high-purity trichlorosilane mixed with high-purity hydrogen that is passed over the rod. Pure silicon (EGS-electronic grade silicon) deposits on the rod as a polycrystalline solid. (Single crystals of Si are later made by subsequently melting the EGS and drawing a single crystal from the melt.) The reaction is H2(g) + SiHCl3(g) → Si(s) + 3 HCl(g) The rod initially has a mass of 1460 g, and the mole fraction of H2 in the exit gas is 0.223. The mole fraction of H2 in the feed to the reactor is 0.580, and the feed enters at the rate of 6.22 kg mol / hr. 1a) Draw and label the system and streams. Clearly label your control volume. 1b) List and count all Unknowns. 1c) List and count all independent Equations. Clearly write out the element balance for each atomic species (Si, H, Cl). 1d) Determine the Degrees of Freedom (DOF). 1e) Solve for: what will be the mass of the rod at the end of 20 min?

Problem 1 (25 pts) USE ELEMENT BALANCES TO SOLVE. One of the most common commercial methods for the production of pure silicon that is to be used for the manufacture of semiconductors is the Siemens process of chemical vapor deposition (CVD). A chamber contains a heated silicon rod and a mixture of high-purity trichlorosilane mixed with high-purity hydrogen that is passed over the rod. Pure silicon (EGS-electronic grade silicon) deposits on the rod as a polycrystalline solid. (Single crystals of Si are later made by subsequently melting the EGS and drawing a single crystal from the melt.) The reaction is H2(g) + SiHCl3(g) → Si(s) + 3 HCl(g) The rod initially has a mass of 1460 g, and the mole fraction of H2 in the exit gas is 0.223. The mole fraction of H2 in the feed to the reactor is 0.580, and the feed enters at the rate of 6.22 kg mol / hr. 1a) Draw and label the system and streams. Clearly label your control volume. 1b) List and count all Unknowns. 1c) List and count all independent Equations. Clearly write out the element balance for each atomic species (Si, H, Cl). 1d) Determine the Degrees of Freedom (DOF). 1e) Solve for: what will be the mass of the rod at the end of 20 min?
Transcript text: Problem 1 (25 pts) USE ELEMENT BALANCES TO SOLVE. One of the most common commercial methods for the production of pure silicon that is to be used for the manufacture of semiconductors is the Siemens process of chemical vapor deposition (CVD). A chamber contains a heated silicon rod and a mixture of high-purity trichlorosilane mixed with high-purity hydrogen that is passed over the rod. Pure silicon (EGS-electronic grade silicon) deposits on the rod as a polycrystalline solid. (Single crystals of Si are later made by subsequently melting the EGS and drawing a single crystal from the melt.) The reaction is \[ \mathrm{H}_{2}(\mathrm{~g})+\mathrm{SiHCl}_{3}(\mathrm{~g}) \rightarrow \mathrm{Si}(\mathrm{~s})+3 \mathrm{HCl}(\mathrm{~g}) \] The rod initially has a mass of 1460 g , and the mole fraction of $\mathrm{H}_{2}$ in the exit gas is 0.223 . The mole fraction of $\mathrm{H}_{2}$ in the feed to the reactor is 0.580 , and the feed enters at the rate of 6.22 kg $\mathrm{mol} / \mathrm{hr}$. 1a) Draw and label the system and streams. Clearly label your control volume. 1b) List and count all Unknowns. 1c) List and count all independent Equations. Clearly write out the element balance for each atomic species $(\mathrm{Si}, \mathrm{H}, \mathrm{Cl})$. 1d) Determine the Degrees of Freedom (DOF). 1e) Solve for: what will be the mass of the rod at the end of 20 min ?
failed

Solution

failed
failed

Solution Steps

Step 1: Draw and label the system and streams

The system is the reactor containing the silicon rod. The inlet stream contains SiHCl3 and H2. The outlet stream contains HCl, SiHCl3, and H2. Si is deposited on the rod within the reactor.

The control volume encompasses the inside of the reactor. The image provided in the problem statement gives a visual representation.

Step 2: List and count all unknowns

Unknowns are the molar flow rates in the exit stream:

  • nHCl,out
  • nSiHCl3,out
  • nH2,out
  • nSi, deposited (effectively the rate of Si deposition)

Total unknowns: 4

Step 3: List and count all independent equations

We can write elemental balances for Si, H, and Cl. Additionally, we have information relating to the mole fractions of hydrogen, which gives a fourth equation.

  • Si balance: nSiHCl3,in = nSiHCl3,out + nSi,deposited
  • H balance: 2nH2,in + nSiHCl3,in = nSiHCl3,out + 2nH2,out + nHCl,out
  • Cl balance: 3nSiHCl3,in = 3nSiHCl3,out + nHCl,out
  • H2 mole fraction in exit: yH2,out = nH2,out / (nH2,out + nHCl,out + nSiHCl3,out)

Total independent equations: 4

Final Answer:

The first three parts of the provided chemical engineering problem have been solved as requested. The diagram, list of unknowns, and set of independent equations have been identified.

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
A vertebrate that lays a hard-shelled amniotic egg, has feathers for flight and insulation, and is endothermic is called a thecodont, mammal, bird, pterosaur.
failedAnswered
Assume that an airline operates a 158-seat McDonnel Douglas MD-90 on a particular route. Historically, the probability of a passenger showing up for a flight is 91%. 1. Assume that 158 tickets were sold. Let X be the number of passengers who showed up for the flight. a. Describe the distribution of X : X ~ ? (n=158, p=0.91) b. Find the probability that the flight is not full, in other words, find the probability that not all passengers will show up: P(X ≤ 157)=0.9 (Round the answer to 4 decimal places) c. Find the expected number of passengers who show up for the flight: E[X]=142 (Round the answer to the whole number) d. Find the expected number of empty seats by subtracting the E[X] from the plane capacity: 14 (Round the answer to the whole number) 2. Assume that the airline sells 7 more ticket(s). Let Y be the number of passengers who showed up for the flight. a. Describe the distribution of Y : Y ~ ? (n=, p=) b. Find the probability that more passengers will show up than the plane can carry: P(Y> )= (Round the answer to 4 decimal places)
failedAnswered
Use synthetic division to find the result when x^4-10x^2-13x-50 is divided by x+5. Write your answer in the form q(x)+r(x)/d(x), where q(x) is the quotient, r(x) is the remainder, and d(x) is the divisor.
failedAnswered
Suppose that the limit as t approaches 3 of t times g(t) equals 12. Show that the limit as t approaches 3 of g(t) exists and equals 4.
failedAnswered
Read the sentence from paragraph 11. Ive never been a great mover and shaker of the earth. What is the meaning of mover and shaker as it is used in the sentence? A. a great singer and dancer B. a responsible individual C. an influential person D. a fighter for justice