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Sodium tripolyphosphate (Na 5 P 3 O 10 ) is used in many synthetic detergents. Its major effect is to soften the water by complexing Mg 2+ and Ca 2+ ions. It also increases the efficiency of surfactants, or wetting agents that lower a liquid’s surface tension. The K value for the formation of MgP 3 O 10 3− is 4.0 × 10 8 The reaction is Mg 2 + ( a q ) + P 3 O 10 5 − ( a q ) ⇌ MgP 3 O 10 3 − ( a q ) . Calculate the concentration of Mg 2+ in a solution that was originally 50. ppm Mg 2+ (50. mg/L of solution) after 40. g Na 5 P 3 O 10 is added to 1.0 L of the solution.

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Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

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BuyFindarrow_forward

Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 15, Problem 107CP
Textbook Problem
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Sodium tripolyphosphate (Na5P3O10) is used in many synthetic detergents. Its major effect is to soften the water by complexing Mg2+ and Ca2+ ions. It also increases the efficiency of surfactants, or wetting agents that lower a liquid’s surface tension. The K value for the formation of MgP3O103− is 4.0 × 108 The reaction is Mg 2 + ( a q ) + P 3 O 10 5 ( a q ) MgP 3 O 10 3 ( a q ) . Calculate the concentration of Mg2+ in a solution that was originally 50. ppm Mg2+ (50. mg/L of solution) after 40. g Na5P3O10 is added to 1.0 L of the solution.

Interpretation Introduction

Interpretation: The equilibrium constant for the formation of MgP3O103- and its reaction is given. The concentration of Mg2+ in a solution, that was originally 50ppm Mg2+ ( 50mg/L of solution), after the addition of 40g Na5P3O103- to 1L of the solution is to be calculated.

Concept introduction: The solubility product is the mathematical product of the dissolved ion concentration of a substance raised to the power of its stoichiometric coefficients.

Sodium tripolyphosphate is used in many synthetic detergents. Its major effect is to soften the water by complexing the magnesium and calcium ions.

Explanation of Solution

Explanation

To determine: The concentration of Mg2+ in a solution, that was originally 50ppm Mg2+ ( 50mg/L of solution), after the addition of 40g Na5P3O103- to 1L of the solution.

The initial concentration of Mg2+ is 2.1×10-3M_ .

The initial concentration of P3O105- is 0.108M_ .

Molar mass of Mg is 24.305g/mol .

The conversion of mg to g is done as,

1mg=103g

Therefore, the conversion of 50mg/L to g/L is done as,

50mg/L=50×103g/L

Since one mole of Mg contains 24.305g of Mg .

Therefore, the number of mol/L of Mg in 50×103g/L =50×103g/L24.305g/mol=2.1×103mol/L

Therefore, the initial concentration of Mg2+ is 2.1×10-3M_ .

Molar mass of Na5P3O10=367.819g/mol .

Amount of Na5P3O10 is 40g .

Since one mole of Na5P3O10 contains 367.819g of Mg .

Therefore, the number of mol/L of Mg in 40g =40367.819=0.108mol/L_

Therefore, the initial concentration of P3O105- is 0

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Chapter 15 Solutions

Chemistry: An Atoms First Approach
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