   Chapter 3, Problem 124E

Chapter
Section
Textbook Problem

Consider the following unbalanced equation: Ca 3 ( PO 4 ) 2 ( s )   +  H 2 SO 4 ( a q ) → CaSO 4 ( s )   +  H 3 PO 4 ( a q ) What masses of calcium sulfate and phosphoric acid can be produced from the reaction of 1.0 kg calcium phosphate with 1.0 kg concentrated sulfuric acid (98% H2SO4 by mass)?

Interpretation Introduction

Interpretation: The amount of calcium sulfate and phosphoric acid that can be produced from the stated reaction is to be calculated.

Concept introduction: The mass of a substance can be obtained by using the number of moles of the substance present and its molar mass. The formula used to calculate the mass of a given substance is,

Massofthesubstance=(Numberofmoles)×(Molarmassofthesubstance)

To determine: The mass of Calcium sulfate and phosphoric acid that can be formed by the stated reaction.

Explanation

To determine: The balanced form of the stated chemical equation.

According to the law of conservation of mass, mass can neither be created nor destroyed. The mass of reactants is equal to the mass of products formed. Therefore a chemical equation, having lesser number of moles of an element on either side of a reaction, is balanced using appropriate numerical coefficients to satisfy the law of conservation of mass.

The given reaction is,

Ca3(PO4)2(s)+H2SO4(aq)CaSO4(s)+H3PO4(aq)

Adding the coefficient 3 to CaSO4 balances the number of atoms of calcium present on either side of the reaction. The equation thus obtained is,

Ca3(PO4)2(s)+3H2SO4(aq)3CaSO4(s)+H3PO4(aq)

Adding the coefficient 3 to H2SO4 and the coefficient 2 to H3PO4 balances the number of atoms of phosphorus, hydrogen and oxygen present on either side of the reaction. The balanced equation thus obtained is,

Ca3(PO4)2(s)+3H2SO4(aq)3CaSO4(s)+2H3PO4(aq)

Given

The balanced chemical reaction is,

Ca3(PO4)2(s)+3H2SO4(aq)3CaSO4(s)+2H3PO4(aq)

The given mass of Ca3(PO4)2 is 1.0kg(1000g) .

The given mass of concentrated H2SO4 is 1.0kg(1000g) .

The given amount of concentrated sulfuric acid is given to have 98% sulfuric acid by mass.

Therefore, the mass of sulfuric acid =(98100×1.0)kg=0.98kg

The molar mass of Ca3(PO4)2 =3Ca+2P+8O=((3×40)+(2×31)+(8×16))g/mol=310g/mol

The molar mass of H2SO4 =2H+S+4O=((2×1)+32+(4×16))g/mol=98g/mol

Formula

The number of moles of a substance is calculated by the formula,

Numberofmoles=GivenmassofthesubstanceMolarmassofthesubstance

Substitute the value of the given mass and the molar mass of Ca3(PO4)2 and H2SO4 in the above expression.

NumberofmolesofCa3(PO4)2=1000kg310g/mol=3.2mol

NumberofmolesofH2SO4=1000kg98g/mol=10.2mol

According to the stated reaction,

1mol of Ca3(PO4)2 reacts with 3mol of H2SO4

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