1. Module 5 Intro

1.12. Page 2

Lesson 2

Module 5—Acids and Bases

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The pH Scale

 

In previous science courses, you may have measured and commented on the pH of solutions, but did you really know what that measurement meant? You may recall the following criteria that are often used to classify acidic, basic, and neutral solutions:

 

If [H3O+(aq)] = [OH-(aq)], then the solution is neutral.
If [H3O+(aq)] > [OH-(aq)], then the solution is acidic.
If [H3O+(aq)] < [OH-(aq)], then the solution is basic.

 

To learn more about the pH scale and what the values on this scale mean in terms of hydronium-ion and hydroxide-ion concentrations, read pages 238 and 239 of “6.2 pH and pOH Calculations” in your textbook.
 
Use “Figure 3” on page 239 to answer “Practice” questions 1 to 3. Check your answers with those given at the back of the textbook.

 

Calculating pH

 

Read pages 240 to 242 in your textbook. Carefully work through the “SAMPLE problems” and “COMMUNICATION examples” presented, as well as the examples below.

 

A pH value is an expression of the hydronium-ion concentration for a solution. Since hydronium-ion concentrations are often small, the most convenient way to represent these values is as a negative logarithm. To convert a hydronium-ion concentration into a pH value, the following algorithm is used:

 

 

To convert a pH value back into a hydronium-ion concentration, the following algorithm is used:

 

 

Earlier, you were asked to express values using the appropriate number of significant digits. The number of digits following the decimal point of a pH value equals the number of significant digits in the hydronium-ion concentration.

 

Work through the next four examples. Examples 1 and 2 provide a multimedia activity that shows how to perform the calculations using a graphing calculator.

 

Example 1

 

A solution has a hydronium-ion concentration of 2.5 × 10−9 mol/L. Calculate the pH of this solution.

Since the hydronium-ion concentration is given, use the formula for pH.

 

 

Substitute the hydronium-ion concentration into the formula.

 

 

Click here to see how this calculation is performed on the TI-83 Plus graphing calculator.

 

Example 2

 

A solution has a pH of 3.5. Determine the hydronium-ion concentration.

Since the pH is given, use the algorithm


Substitute the pH value into the algorithm.

 

 

Click here to see how this calculation is performed on the TI-83 Plus graphing calculator.

 

A photograph shows the display screen of a calculator. The first line reads ten caret negative sign zero decimal zero zero. The second line reads one.

Example 3

 

Calculate the hydronium-ion concentration, [H3O+(aq)], for a solution with a pH of 0.00.

 


Example 4

 

Compare the hydronium-ion concentrations of a solution with a pH of 3.0 with that of a solution with a pH of 4.0.

 

A photograph shows the display screen of a calculator. The first line reads ten caret negative sign three decimal zero. The second line reads decimal zero zero zero one. The third line reads ten caret negative sign four decimal zero. The fourth line reads one E negative four. The fifth line reads decimal zero zero one divided by one E negative four. The sixth line reads ten.

Step 1: Calculate the hydronium-ion concentration in the solution with a pH of 3.0.

 

 

Step 2: Calculate the hydronium-ion concentration in a solution with a pH of 4.0.

 


Step 3: Determine how many times greater the hydronium-ion concentration is between the two solutions. Divide the greater concentration value by the lesser value.

 

 

The hydronium-ion concentration of a solution with a pH of 3.0 is ten times greater than the hydronium-ion concentration of a solution with a pH of 4.0.

 

Self-Check

 

SC 1. Calculate the pH of a solution with a hydronium-ion concentration of 4.70 × 10−4 mol/L.

 

SC 2. Determine the hydronium-ion concentration for a solution with a pH of 0.13.

 

SC 3. Calculate the pH of a solution of hydrobromic acid that has a hydronium-ion concentration of 6.9 × 10−5 mol/L.

 

SC 4. Is it possible for a solution to have negative pH values or pH values over 14? Use calculations to justify your answer.

 

Check your work.
Self-Check Answers

 

SC 1.

 


A photograph shows the display for a calculator. The first line reads negative sign log bracket four decimal seven zero E negative four bracket. The second line reads three decimal three two seven nine zero two one four two.

 


SC 2.

 


A photograph shows the display for a calculator. The first line reads ten caret negative sign zero decimal one three. The second line reads decimal seven four one three one zero two four one three.

SC 3.

 


A photograph shows the display for a calculator. The first line reads negative sign log bracket six decimal nine E negative five bracket. The second line reads four decimal one six one one five zero nine zero nine.


SC 4. Yes. A solution with a negative pH value has a hydronium-ion concentration that is greater than 1.0 mol/L. A solution with a pH value over 14 has a hydronium-ion concentration that is less than 1.0 × 10−14 mol/L. Both concentrations are possible.