Silane, \(\mathrm{SiH}_{4}\), is the silicon analogue of methane, \(\mathrm{CH}_{4}\). It is prepared industrially according to the following equations: $$ \begin{aligned} \mathrm{Si}(s)+3 \mathrm{HCl}(g) & \longrightarrow \operatorname{HSiCl}_{3}(l)+\mathrm{H}_{2}(g) \\ 4 \mathrm{HSiCl}_{3}(l) & \longrightarrow \mathrm{SiH}_{4}(g)+3 \mathrm{SiCl}_{4}(l) \end{aligned} $$ a. If \(156 \mathrm{~mL} \mathrm{HSiCl}_{3}(d=1.34 \mathrm{~g} / \mathrm{mL})\) is isolated when \(15.0 \mathrm{~L}\) \(\mathrm{HCl}\) at \(10.0 \mathrm{~atm}\) and \(35^{\circ} \mathrm{C}\) is used, what is the percent yield of \(\mathrm{HSiCl}_{3}\) ? b. When \(156 \mathrm{~mL} \mathrm{HSiCl}_{3}\) is heated, what volume of \(\mathrm{SiH}_{4}\) at \(10.0\) atm and \(35^{\circ} \mathrm{C}\) will be obtained if the percent yield of the reaction is \(93.1 \%\) ?

Step by step solution

01

Determine moles of HCl used

First, we will use the ideal gas law (PV = nRT) to find the moles of HCl used in the reaction. Given the volume, pressure, and temperature of HCl, and using the gas constant R = 0.0821 L·atm/mol·K: n(HCl) = PV / (RT) n(HCl) = (10.0 atm)(15.0 L) / (0.0821 L·atm/mol·K)(308 K) n(HCl) = 6.11 mol

02

Calculate theoretical moles of HSiCl3 produced

Use stoichiometry to determine the theoretical moles of HSiCl3 that could be produced from the given moles of HCl: The balanced chemical equation is: Si(s) + 3HCl(g) -> HSiCl3(l) + H2(g) From the stoichiometry, 3 moles of HCl are needed to produce 1 mole of HSiCl3. Therefore, theoretical moles of HSiCl3 = n(HCl) / 3 = 6.11 mol HCl / 3 = 2.037 mol HSiCl3

03

Calculate actual moles of HSiCl3 produced

Given the volume and density of HSiCl3 produced, we can find its mass and convert it to moles. The molar mass of HSiCl3 is: 1(28.09 g/mol) + 1(1.01 g/mol) + 3(35.45 g/mol) = 144.45 g/mol. Mass of HSiCl3 = Volume x Density = 156 mL x 1.34 g/mL = 209.04 g Now, convert the mass of HSiCl3 to moles: Actual moles of HSiCl3 = mass / molar mass = 209.04 g / 144.45 g/mol = 1.447 mol

04

Calculate the percent yield of HSiCl3

Percent yield = (actual moles / theoretical moles) x 100 Percent yield of HSiCl3 = (1.447 mol / 2.037 mol) x 100 = 71.0%

05

Calculate the moles of SiH4 produced

The balanced chemical equation for the second step is: 4HSiCl3(l) -> SiH4(g) + 3SiCl4(l) From the stoichiometry, 4 moles of HSiCl3 are needed to produce 1 mole of SiH4. We are also given a percent yield of 93.1% for this reaction. Use the percent yield and the actual moles of HSiCl3 to calculate the moles of SiH4 produced: Moles of SiH4 = (Actual moles of HSiCl3)(Percent yield / 100) x (1 mol SiH4 / 4 mol HSiCl3) Moles of SiH4 = (1.447 mol)(93.1/100) x (1/4) = 0.337 mol SiH4

06

Calculate the volume of SiH4 produced

Use the ideal gas law (PV = nRT) to calculate the volume of SiH4 produced at 10.0 atm and 35°C: Volume of SiH4 = n(RT) / P Volume of SiH4 = (0.337 mol)(0.0821 L·atm/mol·K)(308 K) / 10.0 atm Volume of SiH4 = 8.57 L Results: a. The percent yield of HSiCl3 is 71.0%. b. The volume of SiH4 produced at 10.0 atm and 35°C is 8.57 L.

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