   Chapter 14, Problem 70E

Chapter
Section
Textbook Problem

# A typical aspirin tablet contains 325 mg acetylsalicylic acid (HC9H7O4). Calculate the pH of a solution that is prepared by dissolving two aspirin tablets in enough water to make one cup (237 mL) of solution. Assume the aspirin tablets are pure acetylsalicylic acid, Ka = 3.3 × 10−4.

Interpretation Introduction

Interpretation: The pH of the given solution, prepared by dissolving two aspirin tablets in enough water to make 237mL of solution, is to be calculated.

Concept introduction: The pH of a solution is define as a figure that expresses the acidity of the alkalinity of a given solution.

The pH of a solution is calculated by the formula, pH=log[H+]

At equilibrium, the equilibrium constant expression is expressed by the formula,

Ka=ConcentrationofproductsConcentrationofreactants

Explanation

Explanation

To determine: The pH of the given solution, prepared by dissolving two aspirin tablets in enough water to make 237mL of solution.

The equilibrium constant expression for the stated dissociation reaction is,

Ka=[H+][C9H7O4][HC9H7O4]

The dominant equilibrium reaction for the given case is,

HC9H7O4(aq)H+(aq)+C9H7O4(aq)

At equilibrium, the equilibrium constant expression is expressed by the formula,

Ka=ConcentrationofproductsConcentrationofreactants

Where,

• Ka is the acid dissociation constant.

The equilibrium constant expression for the given reaction is,

Ka=[H+][C9H7O4][HC9H7O4] (1)

The number of moles of HC9H7O4 is 3.61×10-3mol_ .

The mass of one aspirin tablet is 325mg .

The mass of two aspirin tablets =(2×325)mg=650mg=0.650g

The molar mass of HC9H7O4 =9C+8H+4O=((9×12)+(8×1)+(4×16))g/mol=180g/mol

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

Numberofmoles=GivenmassMolarmass

Substitute the value of the given mass and the molar mass of HC9H7O4 in the above expression.

Numberofmoles=0.650g180g/mol=3.61×10-3mol_

The initial [HC9H7O4] is 0.015M_ .

The calculated number of moles of HC9H7O4 is 3.61×103mol .

The total volume is 237mL(0.237L) .

The concentration is calculated by the formula,

Concentration=NumberofmolesVolume(L)

Substitute the value of the number of moles of HC9H7O4 and the volume in the above expression.

Concentration=3.61×103mol0.237L=0.015M_

The [H+] is 2

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