Question

Phosphine gas reacts with oxygen according to the following equation: $$ 4 \mathrm{PH}_{3}(g)+8 \mathrm{O}_{2}(g) \longrightarrow \mathrm{P}_{4} \mathrm{O}_{10}(s)+6 \mathrm{H}_{2} \mathrm{O}(g) $$ Calculate (a) the mass of tetraphosphorus decaoxide produced from \(12.43 \mathrm{~mol}\) of phosphine. (b) the mass of \(\mathrm{PH}_{3}\) required to form \(0.739 \mathrm{~mol}\) of steam. (c) the mass of oxygen gas that yields \(1.000 \mathrm{~g}\) of steam. (d) the mass of oxygen required to react with \(20.50 \mathrm{~g}\) of phosphine.

Short answer

Question: Calculate the mass of tetraphosphorus decaoxide produced from 12.43 mol of phosphine. Answer: Step 1: Calculate the moles of P4O10 produced: Moles of P4O10 = (moles of PH3) / 4 = (12.43) / 4 = 3.1075 mol Step 2: Calculate the mass of P4O10 produced: Mass of P4O10 = (moles of P4O10) × (molecular weight of P4O10) = (3.1075) × (283.88 g/mol) = 882.77 g The mass of tetraphosphorus decaoxide produced from 12.43 mol of phosphine is 882.77 g.

Step-by-step solution

Find moles of P4O10 produced

According to the stoichiometry of the balanced equation, the ratio of moles of PH3 to moles of P4O10 is 4:1. Therefore, the moles of P4O10 produced can be calculated as: $$ \text{moles of P}_{4}\text{O}_{10} = \frac{\text{moles of PH}_{3}}{4} = \frac{12.43}{4} $$

Calculate mass of P4O10 produced

After finding the moles of P4O10, multiply the moles with the molecular weight of P4O10 to find the mass. $$ \text{mass of P}_{4}\text{O}_{10} = \text{moles of P}_{4}\text{O}_{10} \times \text{molecular weight of P}_{4}\text{O}_{10} $$ Molecular weight of P4O10 = 4(30.97) + 10(16.00) = 283.88 g/mol $$ \text{mass of P}_{4}\text{O}_{10} = \frac{12.43}{4} \times 283.88 $$ (b) Calculate the mass of PH3 required to form 0.739 mol of steam.

Find moles of PH3 required

According to the stoichiometry of the balanced equation, the ratio of moles of PH3 to moles of H2O is 4:6. Therefore, the moles of PH3 required can be calculated as: $$ \text{moles of PH}_{3} = \frac{4}{6} \times \text{moles of H}_{2}\text{O} = \frac{2}{3} \times 0.739 $$

Calculate mass of PH3 required

After finding the moles of PH3, multiply the moles with the molecular weight of PH3 to find the mass. $$ \text{mass of PH}_{3} = \text{moles of PH}_{3} \times \text{molecular weight of PH}_{3} $$ Molecular weight of PH3 = 1(30.97) + 3(1.01) = 33.99 g/mol $$ \text{mass of PH}_{3} = \frac{2}{3} \times 0.739 \times 33.99 $$ (c) Calculate the mass of oxygen gas that yields 1.000 g of steam.

Find moles of O2 required

According to the stoichiometry of the balanced equation, the ratio of moles of O2 to moles of H2O is 8:6. First, find the moles of H2O from its mass: $$ \text{moles of H}_{2}\text{O} = \frac{\text{mass of H}_{2}\text{O}}{\text{molecular weight of H}_{2}\text{O}} = \frac{1.000}{18.02} $$ Now, find the moles of O2 required: $$ \text{moles of O}_{2} = \frac{8}{6} \times \text{moles of H}_{2}\text{O} = \frac{4}{3} \times \frac{1.000}{18.02} $$

Calculate mass of O2 required

After finding the moles of O2, multiply the moles with the molecular weight of O2 to find the mass. $$ \text{mass of O}_{2} = \text{moles of O}_{2} \times \text{molecular weight of O}_{2} $$ Molecular weight of O2 = 2(16.00) = 32.00 g/mol $$ \text{mass of O}_{2} = \frac{4}{3} \times \frac{1.000}{18.02} \times 32.00 $$ (d) Calculate the mass of oxygen required to react with 20.50 g of phosphine.

Find moles of O2 required

First, find the moles of PH3 from its mass: $$ \text{moles of PH}_{3} = \frac{\text{mass of PH}_{3}}{\text{molecular weight of PH}_{3}} = \frac{20.50}{33.99} $$ According to the stoichiometry of the balanced equation, the ratio of moles of O2 to moles of PH3 is 8:4. Therfore, the moles of O2 required can be calculated as: $$ \text{moles of O}_{2} = 2 \times \text{moles of PH}_{3} = 2 \times \frac{20.50}{33.99} $$

Calculate mass of O2 required

After finding the moles of O2, multiply the moles with the molecular weight of O2 to find the mass. $$ \text{mass of O}_{2} = \text{moles of O}_{2} \times \text{molecular weight of O}_{2} = 2 \times \frac{20.50}{33.99} \times 32.00 $$