Question In Description

Question

An engineer used the reaction below to generate SiF4 gas. How Many liters of SiF4 gas could she generate by reacting 75 grams of HF with an excess of SIO2, if the pressure of the SiF4 is 745 torr at a temperature of 27°C?

Show work, use gas stoicheometry

Answer 1

This question is based around the ideal gas law: PV = nRT

Thinking about SiF₄ we are given a temperature and pressure but no mass/moles (where R is a constant 0.08206 L•atm•K^-1•mol^-1 and volume is what we are trying to calculate). This then presents a situation where we need to determine the moles of SiF₄ produced to be able to calculate the volume of SiF₄ produced. The moles of SiF₄ can be calculated from the balanced reaction equation:

4HF + SiO₂ ---> SiF₄ + 2H₂O

We are told 75 g of HF react with excess SiO₂. Therefore, HF is our limiting reagent in the formation of SiF₄. Thus, we can assumed 100% of our HF reacts and is converted into SiF₄. Using stoichiometry we can then calculate the moles of SiF₄ from the original mass of HF. We will also need the molar mass of HF which can be calculated from the individual atom's weights on the periodic table:

H molar mass: 1.008 g/mol

F molar mass: 18.998 g/mol

HF molar mass = 1.008 g/mol + 18.998 g/mol = 20.006 g/mol

75 g HF ÷ 20.006 g/mol = 3.75 mol HF

3.75 mol HF x (1 mol SiF₄/4 mol HF) = 0.937 mol SiF₄

Note that the (1 mol SiF₄/4 mol HF) term came from our balanced reaction equation

Now that we have our moles of SiF₄ produced we can calculate the volume of space it would occupy according to the ideal gas law. However, it should be noted that our constant term has units of L•atm•K^-1•mol^-1 while some of the information we're given in the problem has different units. It is very important to keep units consistent and we must therefore do some unit conversion before calculating the volume of SiF₄ produced:

745 torr ÷ 760 torr/atm = 0.980 atm SiF₄

27 °C + 273 = 300 K

(0.980 atm)V=(0.937 mol)(0.08206 L•atm•K^-1•mol^-1)(300 K)

V = 23.5 L SiF₄