Question

a. Describe what is meant by the pH of a solution. b. Write the equation for determining pH. c. Explain and illustrate what is meant by the common logarithm of a number.

Short answer

pH is a measure of acidity or alkalinity, defined as \(\text{pH} = -\text{log}_{10}[H^+]\). The common logarithm is the logarithm to the base 10.

Step-by-step solution

- Definition of pH

The pH of a solution is a measure of its acidity or alkalinity. It is defined as the negative logarithm (base 10) of the hydrogen ion concentration \([H^+]\) in the solution. The pH scale typically ranges from 0 to 14, where a pH of 7 is neutral, a pH less than 7 is acidic, and a pH greater than 7 is basic.

- pH Equation

The equation for determining the pH of a solution is given by: \[\text{pH} = -\text{log}_{10}[H^+]\] where \([H^+]\) is the concentration of hydrogen ions in moles per liter.

- Definition of Common Logarithm

The common logarithm of a number is the logarithm to the base 10. It is often denoted as \(\text{log}_{10}\). For example, the common logarithm of 100 is 2 because \(\text{log}_{10} 100 = 2\), meaning that 10 raised to the power of 2 equals 100. Similarly, the common logarithm of 1000 is 3 because \(\text{log}_{10} 1000 = 3\).

Key concepts

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The concept of acidity is essential in understanding the pH of a solution. In simple terms, acidity refers to how acidic or basic a substance is. When a substance dissolves in water, it can release hydrogen ions \(H^+\). The number of these ions determines the acidity of the solution.

More hydrogen ions mean higher acidity, less hydrogen ions mean lower acidity. For example, lemon juice is acidic because it has a lot of hydrogen ions, while soap is basic because it has very few.

Acids usually taste sour and can be corrosive. Bases, or alkalines, are often slippery and can neutralize acids. Understanding acidity helps us navigate everyday substances and their properties.

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The term 'common logarithm' might sound complex, but it's actually quite simple. Common logarithms are logarithms with a base of 10. In mathematical notation, it's written as log\( \text 10 \).

For instance, let's look at the common logarithm of 100. We write that as log \(100 \), and its value is 2. This means \(10^2 = 100 \). So, the logarithm tells us the power or exponent needed to get from 10 to 100.

Similarly, for 1000, log \(1000 \) equals 3 because 10 raised to the power of 3 equals 1000. This notion helps simplify calculations with large numbers, making it an essential tool in both science and math.

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Hydrogen ion concentration is a key concept in determining the pH of a solution. The concentration refers to the amount of hydrogen ions present in a solution. It's usually measured in moles per liter (M).

The more hydrogen ions there are, the more acidic the solution will be. Conversely, fewer hydrogen ions mean a less acidic (or more basic) solution.

For example, if a solution has a hydrogen ion concentration of \(1 x 10^{-4} M\), it is more acidic than a solution with a concentration of \(1 x 10^{-7} M\). This measure is crucial for understanding chemical reactions and maintaining the balance in various environments.

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The pH scale is a numerical representation of how acidic or basic a solution is. The scale ranges from 0 to 14.

A pH of 7 is considered neutral, meaning the solution is neither acidic nor basic. Water is a common example of a neutral substance. Solutions with a pH less than 7 are acidic, and those with a pH greater than 7 are basic or alkaline.

For instance, lemon juice has a pH of about 2, making it very acidic. On the other hand, baking soda has a pH of around 9, making it slightly basic. Using the pH scale, scientists and students can quickly understand the nature of a solution and predict how it will react with other substances.