   # A solution is prepared by adding 50.0 mL concentrated hydrochloric acid and 20.0 mL concentrated nitric acid to 300 mL water. More water is added until the final volume is 1.00 L. Calculate [H + ], [OH − ], and the pH for this solution. [ Hint: Concentrated HCl is 38% HCl (by mass) and has a density of 1.19 g/mL; concentrated HNO 3 is 70.% HNO 3 (by mass) and has a density of 1.42 g/mL. ### Chemistry: An Atoms First Approach

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

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 13, Problem 62E
Textbook Problem
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## A solution is prepared by adding 50.0 mL concentrated hydrochloric acid and 20.0 mL concentrated nitric acid to 300 mL water. More water is added until the final volume is 1.00 L. Calculate [H+], [OH−], and the pH for this solution. [Hint: Concentrated HCl is 38% HCl (by mass) and has a density of 1.19 g/mL; concentrated HNO3 is 70.% HNO3 (by mass) and has a density of 1.42 g/mL.

Interpretation Introduction

Interpretation: The pH,[H+] and [OH] of the given solution made by adding 50.0mL concentrated hydrochloric acid and 20.0mL concentrated nitric acid to 300mL water (more water added to make the volume 1L ) 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. A logarithmic scale is used on which, the value 7 corresponds to a neutral species, a value less than 7 corresponds to an acid and a value greater than 7 corresponds to a base.

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

The sum, pH+pOH=14

The equilibrium constant for water is denoted by Kw and is expressed as,

Kw=[H+][OH]

### Explanation of Solution

Explanation

To determine: The pH,[H+] and [OH] of the given solution.

The moles of HCl are 0.620mol_ and that of HNO3 are 0.316mol_ .

Given

Volume of concentrated HCl is 50.0mL(0.050L) .

Mass percent of concentrated HCl is 38% .

The density of concentrated HCl is 1.19g/mL .

Volume of concentrated HNO3 is 20.0mL(0.020L) .

Mass percent of concentrated HNO3 is 70% .

The density of concentrated HNO3 is 1.42g/mL .

The molar mass of HCl =H+Cl=(1+35.5)g/mol=36.5g/mol

The molar mass of HNO3 =H+N+3O=(1+14+(3×16))g/mol=63g/mol

The number of moles is calculated by the formula,

Molesofsolute=Volume×Density×Percentmass×1Molarmass

Substitute the value of volume, percent mass, molar mass and density of HCl and HNO3 in the above expression.

For HCl ,

MolesofHCl=(50.0mL)×(1.19g/mol)×(38100)×1(36.5g/mol)=0.620mol_

For HNO3 ,

MolesofHNO3=(20.0mL)×(1.42g/mol)×(70100)×1(63g/mol)=0.316mol_

The [H+] is 0.936M_ .

The total volume of the solution is given to be 1L .

Both the given acids are strong acids. Therefore, these will dissociate completely to form [H+] ions

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