   Chapter 16, Problem 100CP

Chapter
Section
Textbook Problem

# Consider a solution made by mixing 500.0 mL of 4.0 M NH3 and 500.0 mL of 0.40 M AgNO3. Ag+ reacts with NH3 to form AgNH3+ and Ag(NH3)2+:   Ag + ( a q )   +   N H 3 ( a q )   ⇌   A g N H 3 + ( a q ) K 1   =   2.1   ×   10 3 AgNH 3 + ( a q )   +   N H 3 ( a q )   ⇌   A g ( N H 3 ) 2 + ( a q )   K 2   = 8.   2   ×   10 3 Determine the concentration of all species in solution.

Interpretation Introduction

Interpretation: The concentration of all the species in the given reaction is to be calculated.

Concept introduction: The solubility product is the mathematical product of a substance’s dissolved ion concentration raised to its power of its stoichiometric coefficients. When sparingly soluble ionic compound releases ions in the solution, it gives relevant solubility product. The solvent is generally water.

Explanation

Explanation

To determine: The concentration of all the species in the given reaction.

The equilibrium constant of the equation (3) is 1.7×107_ .

The given equilibrium reactions are,

Ag++NH3AgNH3+K1=2.1×103 (1)

AgNH3++NH3Ag(NH3)2+K2=8.2×103 (2)

The net equilibrium reaction for the mixture is calculated by adding equation (1) and equation (2) which is,

Ag++2NH3Ag(NH3)2+ (3)

The equilibrium constant for the reaction is calculates by the formula,

K=K1×K2

Where,

• K is the equilibrium constant of equation (3).
• K1 is the equilibrium constant of equation (1).
• K2 is the equilibrium constant of equation (2).

Substitute the value of K1 and K2 in the above formula.

K=2.1×103×8.2×103=1.7×107_

The [Ag+]=4.6×10-9M_ .

The [NH3]=1.6M_ .

The [Ag(NH3)2+]=0.20M_ .

The initial concentration of [Ag+] and [NH3] would be half because equal volume of two solutions are mixed.

The change in concentration of species at equilibrium is assumed to be x . The ICE table for the reaction is,

Ag++2NH3Ag(NH3)2+Before0.20M0.20M0Change01.60.20Equilibriumx1.6+2x0

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