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Chapter 4: Problem 89

High-purity silicon is obtained using a three-step process. The first step involves heating solid silicon dioxide, \(\mathrm{SiO}_{2^{\prime}}\) with solid carbon to give solid silicon and carbon monoxide gas. In the second step, solid silicon is converted into liquid silicon tetrachloride, \(\mathrm{SiCl}_{4}\) by treating it with chlorine gas. In the last step, \(\mathrm{SiCl}_{4}\) is treated with hydrogen gas to give ultrapure solid silicon and hydrogen chloride gas. (a) Write balanced chemical equations for the steps involved in this three- step process. (b) Calculate the masses of carbon, chlorine, and hydrogen required per kilogram of silicon.

Short Answer

Expert verified
Balanced chemical equations: 1) \( \mathrm{SiO}_{2} + 2C \rightarrow Si + 2CO \), 2) \( Si + 2Cl_{2} \rightarrow SiCl_{4} \), 3) \( SiCl_{4} + 2H_{2} \rightarrow Si + 4HCl \). Masses required per kg of silicon: Carbon = \( \frac{1000}{28} \times 2 \times 12 \) grams, Chlorine = \( \frac{1000}{28} \times 2 \times 71 \) grams, Hydrogen = \( \frac{1000}{28} \times 2 \times 2 \) grams.

Step by step solution

01

Balance the chemical equations

Write the chemical reactions for each step and balance them. For step one, the reaction is: \[ \mathrm{SiO}_{2} + 2C \rightarrow Si + 2CO \] For step two, the reaction is: \[ Si + 2Cl_{2} \rightarrow SiCl_{4} \] And for step three, we have: \[ SiCl_{4} + 2H_{2} \rightarrow Si + 4HCl \]
02

Stoichiometry calculations for carbon

For each kg (or 1000 grams) of silicon, how many grams of carbon are needed? Looking at the first balanced equation, you can see that one mole of Si requires 2 moles of C to produce. The molar mass of Si is approximately 28 grams/mole and for C, it's about 12 grams/mole. Therefore, \[ \frac{1000}{28} \] moles of Si require \[ \frac{1000}{28} \times 2 \] moles of C, which equates to \[ \frac{1000}{28} \times 2 \times 12 \] grams of C.
03

Stoichiometry calculations for chlorine and hydrogen

Next, determine the mass of chlorine and hydrogen required per kg of silicon. From the second and third balanced equations, it can be seen that one mole of Si requires 2 moles of \( Cl_{2} \) and 2 moles of \( H_{2} \) respectively. The molar mass of \( Cl_{2} \) is approximately 71 grams/mole and for \( H_{2} \), it's about 2 grams/mole. Therefore, \[ \frac{1000}{28} \] moles of Si require \[ \frac{1000}{28} \times 2 \] moles of \( Cl_{2} \) and \( H_{2} \), which equates to \[ \frac{1000}{28} \times 2 \times 71 \] grams of \( Cl_{2} \) and \[ \frac{1000}{28} \times 2 \times 2 \] grams of \( H_{2} \) respectively.

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Most popular questions from this chapter

Ammonia can be generated by heating together the solids \(\mathrm{NH}_{4} \mathrm{Cl}\) and \(\mathrm{Ca}(\mathrm{OH})_{2} . \mathrm{CaCl}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) are also formed. (a) If a mixture containing \(33.0 \mathrm{g}\) each of \(\mathrm{NH}_{4} \mathrm{Cl}\) and \(\mathrm{Ca}(\mathrm{OH})_{2}\) is heated, how many grams of \(\mathrm{NH}_{3}\) will form? (b) Which reactant remains in excess, and in what mass?

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