   Chapter 14, Problem 23Q

Chapter
Section
Textbook Problem

# How many significant figures are there in the following numbers: 10.78, 6.78, 0.78? If these were pH values, to how many significant figures can you express the [H+]? Explain any discrepancies between your answers to the two questions.

Interpretation Introduction

Interpretation: The number of significant figures present in each of the given numbers is to be determined. If the given numbers were pH values, the number of significant figures that can be expressed as [H+] and the discrepancies in these answers are to be stated.

Concept introduction: The total number of single digits used in expressing a number is known as significant figures. The rules for counting significant figures are,

• All non-zero numbers are significant.
• The zeros occurring between two significant numbers are significant.
• The trailing zeros, present in a decimal value, are the only significant ones.
Explanation

Explanation

To determine: The number of significant figures present in each of the given numbers 10.78,6.78 and 0.78 ; if these are pH values, the number of significant figures that can be expressed as [H+] ; discrepancies between the two answers.

The number of significant figures present in 10.78 is four.

According to the rules for counting the number of significant figures, all non-zero numbers are significant and zeros occurring between two significant numbers are significant. Hence, the number 10.78 has four significant figures.

The number of significant figures present in 6.78 is three.

According to the rules for counting the number of significant figures, all non-zero numbers are significant. Hence, the number 6.78 has three significant figures.

The number of significant figures present in 0.78 is two.

According to the rules for counting the number of significant figures, all non-zero numbers are significant. Hence, the number 0.78 has two significant figures.

The number of significant figures present in [H+] of pH=10.78 is five.

Given

The value of pH is 10.78 .

Formula

The concentration of [H+] is calculated using the formula,

pH=log10[H+]

Substitute the value of pH in above equation.

pH=log10[H+]10.78=log10[H+][H+]=1.6596×1011

The significant figures in terms of pH value,

• The number of significant figures in pH is same as the number of decimal places in the [H+] .

The number of significant figure in pH is four and the significant figures after the decimal in 1.6596×1011 are four. Hence, total significant figure in [H+] value is five.

The number of significant figures present in [H+] of pH=6.78 is four.

Given

The value of pH is 6.78 .

Formula

The concentration of [H+] is calculated using the formula,

pH=log10[H+]

Substitute the value of pH in above equation

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