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Chapter 3: Problem 126

Consider the following unbalanced reaction: $$ \mathrm{P}_{4}(s)+\mathrm{F}_{2}(g) \longrightarrow \mathrm{PF}_{3}(g) $$ What mass of \(\mathrm{F}_{2}\) is needed to produce \(120 . \mathrm{g}\) of \(\mathrm{PF}_{3}\) if the reaction has a \(78.1 \%\) yield?

Short Answer

Expert verified
Hence, \(98.97 \textrm{ g}\) of \(\textrm{F}_2\) are needed to produce \(120 \textrm{ g}\) of \(\textrm{PF}_3\) with a \(78.1\%\) yield.

Step by step solution

01

Balance the chemical equation.

The given chemical equation is: \( \textrm{P}_4(s) + \textrm{F}_2(g) \longrightarrow \textrm{PF}_3(g) \) Balancing the chemical equation, we get: \( \textrm{P}_4(s) + 6\textrm{F}_2(g) \longrightarrow 4\textrm{PF}_3(g) \)
02

Obtain the stoichiometric ratio.

From the balanced chemical equation, the stoichiometric ratios are: 1 mol P4 : 6 mol F2 : 4 mol PF3
03

Calculate the moles of PF3 formed.

Given the mass of PF3 is 120 g, let's find the number of moles using the molar mass of PF3 (1P + 3F = 1 × 30.97 + 3 × 19.00 = 88.97 g/mol): Moles of PF3 = (mass of PF3) / (molar mass of PF3) moles of PF3 = (120 g) / (88.97 g/mol) = 1.349 mol
04

Use the stoichiometry to find the moles of F2 required.

From the stoichiometric ratio, 1 mol of P4 requires 6 mol of F2 to produce 4 mol of PF3. So, let's calculate the moles of F2 required to produce 1.349 mol of PF3: Moles of F2 needed = (1.349 mol PF3) × (6 mol F2 / 4 mol PF3) = 2.023 mol F2
05

Convert the moles of F2 to mass, considering the yield.

To find mass of F2 needed, we use the molar mass of F2 (2 × 19.00 g/mol = 38.00 g/mol) and the given yield (78.1%): Mass of F2 required = (moles of F2 needed) × (molar mass of F2) × (100 / yield) Mass of F2 required = (2.023 mol) × (38.00 g/mol) × (100 / 78.1) Mass of F2 required = 98.97 g Hence, 98.97 g of F2 are needed to produce 120 g of PF3 with a 78.1% yield.

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Most popular questions from this chapter

Many cereals are made with high moisture content so that the cereal can be formed into various shapes before it is dried. \(\mathrm{A}\) cereal product containing \(58 \% \mathrm{H}_{2} \mathrm{O}\) by mass is produced at the rate of \(1000 . \mathrm{kg} / \mathrm{h}\). What mass of water must be evaporated per hour if the final product contains only \(20 . \%\) water?

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