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 (see Figure P5.3.5) 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) + 3HCl(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. What will be the mass of the rod at the end of 20 min?

Well, well, well, looks like we have a chemistry question in the house! Don't worry, I'm here to infuse some humor into your quest for knowledge.

Let's see what we have here. We're dealing with the Siemens process, some hydrogen gas, and a silicon rod. Sounds like a recipe for scientific success!

To tackle this problem, we'll need to use some good old-fashioned stoichiometry. Remember, stoichiometry is like chocolate cake – it's all about the perfect balance of ingredients!

First, let's calculate the number of moles of H2 in the feed to the reactor. We know that the feed enters at a rate of 6.22 kg mol/hr, but since we're dealing with a 20-minute timeframe, we need to adjust the rate accordingly. So, buckle up, it's time for some math acrobatics!

(6.22 kg mol/hr) / (60 min/hr) = (mass of H2 in 20 min) kilograms

Next, let's figure out the number of moles of H2 in the exit gas. We're given the mole fraction of H2 in the exit gas, so multiplying it by the total number of moles in the exit gas will give us the number of moles of H2.

(mole fraction of H2 in exit gas) * (total number of moles in exit gas) = (number of moles of H2)

Now, here comes the good part. According to the reaction equation, every molecule of H2 will produce one molecule of Si. So, the number of moles of H2 is equal to the number of moles of Si. It's a fair trade, just like trading your last piece of pizza for a high-five!

Finally, we can calculate the change in mass of the rod using the balanced equation. For every mole of Si produced, the mass of the rod will decrease by the molar mass of Si.

Now, let's put on our chemistry hats and start crunching those numbers. Just remember, if you ever feel overwhelmed, just imagine a clown juggling beakers – it always helps!

To find the mass of the rod at the end of 20 minutes, we need to calculate the amount of silicon deposited on the rod during this time.

First, let's calculate the number of moles of H2 in the feed to the reactor:

Number of moles of H2 in the feed = Mole fraction of H2 in the feed * Total moles in the feed
= 0.580 * 6.22 mol/hr

Next, let's calculate the number of moles of SiHCl3 consumed in 20 minutes:

Number of moles of SiHCl3 consumed = Number of moles of H2 consumed / 3
= (Number of moles of H2 in the feed - Number of moles of H2 in the exit gas) / 3
= (0.580 * 6.22 - 0.223 * (6.22 / 1000 * 20)) / 3

Now, let's calculate the mass of silicon deposited on the rod:

Mass of silicon deposited = Number of moles of SiHCl3 consumed * Molar mass of silicon
= Number of moles of SiHCl3 consumed * 28.0855 g/mol

Finally, let's calculate the mass of the rod at the end of 20 minutes:

Mass of the rod at the end of 20 minutes = Initial mass of the rod - Mass of silicon deposited

Note: Make sure to convert the units appropriately to ensure consistent calculations.

To find the mass of the rod at the end of 20 minutes, we need to calculate the amount of silicon that has been deposited on the rod during this time.

First, let's calculate the number of moles of hydrogen consumed during the 20 minutes. We know the mole fraction of hydrogen in the exit gas (0.223) and the mole fraction of hydrogen in the feed (0.580), and we know the feed rate which is given as 6.22 kg mol/hr.

To find the number of moles of hydrogen consumed in 20 minutes, we can use the following equation:

Moles of hydrogen consumed = (Mole fraction of hydrogen in feed - Mole fraction of hydrogen in exit gas) * Feed rate * Time

Let's plug in the given values:

Moles of hydrogen consumed = (0.580 - 0.223) * 6.22 kg mol/hr * (20 min / 60 min)

Now, we need to convert the mass of the hydrogen consumed into the mass of silicon deposited on the rod. According to the balanced chemical equation, 1 mole of silicon is produced for every 3 moles of hydrogen consumed.

To calculate the mass of silicon deposited, we can use the following equation:

Mass of silicon deposited = (Moles of hydrogen consumed / 3) * Molar mass of silicon

The molar mass of silicon is 28.086 g/mol.

Now, we can calculate the mass of silicon deposited:

Mass of silicon deposited = (Moles of hydrogen consumed / 3) * 28.086 g/mol

Finally, to find the mass of the rod at the end of 20 minutes, we subtract the mass of silicon deposited from the initial mass of the rod:

Mass of rod at the end = Initial mass of rod - Mass of silicon deposited

Let's plug in the values and calculate the mass of the rod at the end of 20 minutes.