/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 112 Phosphorus can be prepared from ... [FREE SOLUTION] | 91Ó°ÊÓ

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Phosphorus can be prepared from calcium phosphate by the following reaction: $$\begin{aligned}2 \mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(s)+6 \mathrm{SiO}_{2}(s)+& 10 \mathrm{C}(s) \longrightarrow \\\& 6 \mathrm{CaSiO}_{3}(s)+\mathrm{P}_{4}(s)+10 \mathrm{CO}(g) \end{aligned}$$ Phosphorite is a mineral that contains \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\) plus other non-phosphorus- containing compounds. What is the maximum amount of \(\mathrm{P}_{4}\) that can be produced from \(1.0 \mathrm{kg}\) of phosphorite if the phorphorite sample is \(75 \% \mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\) by mass? Assume an excess of the other reactants.

Short Answer

Expert verified
The maximum amount of Pâ‚„ that can be produced from 1.0 kg of phosphorite is approximately \(149.79 \, \text{g}\).

Step by step solution

01

Calculate the mass of calcium phosphate in the phosphorite sample

Since the phosphorite sample is 75% calcium phosphate by mass, we can calculate the mass of calcium phosphate in the 1.0 kg phosphorite sample as follows: Mass of calcium phosphate = (1.0 kg phosphorite) × (0.75) = 0.75 kg Since we will be dealing with grams throughout the problem, let's convert the mass to grams: 0.75 kg = 750 g
02

Determine the moles of calcium phosphate

To determine the moles of calcium phosphate, we need to find the molar mass of Ca₃(PO₄)₂: Molar mass of Ca₃(PO₄)₂ = (3 × molar mass of Ca) + (2 × molar mass of P) + (8 × molar mass of O) = (3 × 40.08 g/mol) + (2 × 30.97 g/mol) + (8 × 16.00 g/mol) = 310.18 g/mol Now, let's calculate the moles of calcium phosphate in the sample: Moles of Ca₃(PO₄)₂ = (750 g Ca₃(PO₄)₂) / (310.18 g/mol) = 2.418 mol
03

Use stoichiometry to calculate the moles of Pâ‚„ produced

The balanced chemical equation gives us the stoichiometric ratio between the moles of Ca₃(PO₄)₂ and moles of P₄ produced: 2 moles of Ca₃(PO₄)₂ → 1 mole of P₄ Using this ratio, we can calculate the moles of P₄ produced from the moles of Ca₃(PO₄)₂: Moles of P₄ = (1 mol P₄ / 2 mol Ca₃(PO₄)₂) × (2.418 mol Ca₃(PO₄)₂) = 1.209 mol P₄
04

Convert the moles of Pâ‚„ to grams

To find the mass of P₄ produced, we need to find the molar mass of P₄: Molar mass of P₄ = 4 × molar mass of P = 4 × 30.97 g/mol = 123.88 g/mol Now, let's calculate the grams of P₄ produced: Mass of P₄ = (1.209 mol P₄) × (123.88 g/mol) = 149.79 g The maximum amount of P₄ that can be produced from 1.0 kg of phosphorite is approximately 149.79 g.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Chemical Reactions
Chemical reactions are a fascinating process where substances, called reactants, interact to form new substances, known as products. In this particular reaction, phosphorus is prepared from calcium phosphate, silicon dioxide, and carbon. The reaction can be summarized with the chemical equation:- \(2 \mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2} + 6 \mathrm{SiO}_{2} + 10 \mathrm{C} \rightarrow 6 \mathrm{CaSiO}_{3} + \mathrm{P}_{4} + 10 \mathrm{CO}\)This equation shows us that the reactants are calcium phosphate (\(\mathrm{Ca}_3(\mathrm{PO}_4)_2\)), silicon dioxide (\(\mathrm{SiO}_2\)), and carbon (\(\mathrm{C}\)), which combine to form calcium silicate (\(\mathrm{CaSiO}_3\)), phosphorus (\(\mathrm{P}_4\)), and carbon monoxide (\(\mathrm{CO}\)).
Chemical reactions often require a balancing process to reflect the Law of Conservation of Mass, ensuring the same number of each type of atom exists on both sides of the equation.
Molar Mass
Molar mass is an important concept in understanding chemical reactions and stoichiometry. It refers to the mass of one mole of a given substance, usually expressed in grams per mole (g/mol).
To compute the molar mass, you add up the atomic masses of all atoms in a molecule.- For calcium phosphate (\(\mathrm{Ca}_3(\mathrm{PO}_4)_2\)), calculate as follows: - 3 calcium atoms: \(3 \times 40.08\) g/mol - 2 phosphorus atoms: \(2 \times 30.97\) g/mol - 8 oxygen atoms: \(8 \times 16.00\) g/molThus, the molar mass of \(\mathrm{Ca}_3(\mathrm{PO}_4)_2\) is calculated as: \(310.18\) g/mol.
Molar mass allows chemists to convert between the mass of a substance and the amount in moles, which is crucial for using stoichiometry in balancing chemical reactions and determining the amounts of products formed.
Balanced Chemical Equations
Balanced chemical equations are crucial for accurately describing a chemical reaction. They ensure that the amount of each element is conserved, abiding by the Law of Conservation of Mass.
To balance a chemical equation, adjust the coefficients (the numbers before the molecules) so that the number of atoms for each element is the same on both sides of the equation.
In our example, the equation:- \(2 \mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2} + 6 \mathrm{SiO}_{2} + 10 \mathrm{C} \rightarrow 6 \mathrm{CaSiO}_{3} + \mathrm{P}_{4} + 10 \mathrm{CO}\)shows balance as:- 6 calcium and 4 phosphorus atoms on both sides- 24 oxygen atoms and 20 carbon atoms on both sidesBy balancing chemical equations, we can use stoichiometry to predict the amounts of substances consumed and produced in a reaction. This is a crucial tool for solving complex quantitative chemistry problems.

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Most popular questions from this chapter

A compound contains only \(\mathrm{C}, \mathrm{H},\) and \(\mathrm{N}\). Combustion of \(35.0 \mathrm{mg}\) of the compound produces \(33.5 \mathrm{mg} \mathrm{CO}_{2}\) and \(41.1 \mathrm{mg}\) \(\mathrm{H}_{2} \mathrm{O} .\) What is the empirical formula of the compound?

Adipic acid is an organic compound composed of \(49.31 \%\) C, \(43.79 \% \mathrm{O},\) and the rest hydrogen. If the molar mass of adipic acid is \(146.1 \mathrm{g} / \mathrm{mol},\) what are the empirical and molecular formulas for adipic acid?

DDT, an insecticide harmful to fish, birds, and humans, is produced by the following reaction: $$2 \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Cl}+\mathrm{C}_{2} \mathrm{HOCl}_{3} \longrightarrow \mathrm{C}_{14} \mathrm{H}_{9} \mathrm{Cl}_{5}+\mathrm{H}_{2} \mathrm{O}$$ In a government lab, 1142 g of chlorobenzene is reacted with 485 g of chloral. a. What mass of DDT is formed, assuming \(100 \%\) yield? b. Which reactant is limiting? Which is in excess? c. What mass of the excess reactant is left over? d. If the actual yield of DDT is \(200.0 \mathrm{g},\) what is the percent yield?

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Arrange the following substances in order of increasing mass percent of carbon. a. caffeine, \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{N}_{4} \mathrm{O}_{2}\) b. sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) c. ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\)

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