Calculate the pH of each acid solution. Explain how the resulting pH values demonstrate that the pH of an acid solution should carry as many digits to the right of the decimal place as the number of significant figures in the concentration of the solution. [H₃O⁺] = 0.044 M [H₃O⁺] = 0.045 M [H₃O⁺] = 0.046 M

Verified step by step guidance

1. <insert step 1> Start by recalling the formula for calculating pH: \( \text{pH} = -\log[\text{H}_3\text{O}^+] \).
2. <insert step 2> For each given concentration of \([\text{H}_3\text{O}^+]\), substitute the value into the pH formula.
3. <insert step 3> Calculate the logarithm of each concentration value. Remember that the logarithm function will give you a number with a decimal.
4. <insert step 4> Apply the negative sign to the logarithm result to find the pH for each concentration.
5. <insert step 5> Observe the number of significant figures in the concentration (2 significant figures) and ensure that the pH value reflects this by having 2 digits after the decimal point. This demonstrates the rule that the pH should carry as many digits to the right of the decimal as the number of significant figures in the concentration.>

Key Concepts

pH Scale

The pH scale measures the acidity or basicity of a solution, defined as the negative logarithm of the hydrogen ion concentration: pH = -log[H3O+]. A lower pH indicates a more acidic solution, while a higher pH indicates a more basic solution. Understanding the pH scale is essential for calculating and interpreting the acidity of various solutions.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. When performing calculations, the result should reflect the precision of the least precise measurement. In the context of pH calculations, the number of significant figures in the concentration of the acid solution dictates how many decimal places the pH value should have, ensuring accurate representation of the data.

Hydronium Ion Concentration

The concentration of hydronium ions ([H3O+]) in a solution directly influences its pH. For example, a higher concentration of [H3O+] results in a lower pH value, indicating a stronger acid. Understanding how to calculate [H3O+] from given concentrations is crucial for determining the corresponding pH and demonstrating the relationship between concentration and acidity.