Determine the concentration of H₃O⁺ to the correct number of significant figures in a solution with each pH. Describe how these calculations show the relationship between the number of digits to the right of the decimal place in pH and the number of significant figures in concentration. pH = 2.50 pH = 2.51 pH = 2.52

Verified step by step guidance

1. <insert step 1> Start by recalling the relationship between pH and the concentration of hydronium ions, \([H_3O^+]\), which is given by the formula: \(pH = -\log[H_3O^+]\).
2. <insert step 2> To find \([H_3O^+]\), rearrange the formula to solve for \([H_3O^+]\): \([H_3O^+] = 10^{-pH}\).
3. <insert step 3> For each given pH value, substitute the pH into the formula to calculate \([H_3O^+]\). For example, for pH = 2.50, calculate \([H_3O^+] = 10^{-2.50}\).
4. <insert step 4> Perform the calculation for each pH value: pH = 2.50, pH = 2.51, and pH = 2.52, ensuring you use the correct number of significant figures.
5. <insert step 5> Note that the number of decimal places in the pH value determines the number of significant figures in the \([H_3O^+]\) concentration. For example, a pH of 2.50 has two decimal places, so \([H_3O^+]\) should be reported with two significant figures.>

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 (H3O+). A lower pH indicates higher acidity, while a higher pH indicates lower acidity. Each unit change in pH represents a tenfold change in H3O+ concentration, making it a logarithmic scale.

Significant Figures

Significant figures are the digits in a number that contribute to its precision, including all non-zero digits, zeros between significant digits, and trailing zeros in the decimal portion. In calculations involving pH and H3O+ concentration, the number of significant figures in the pH value dictates the precision of the resulting concentration, emphasizing the importance of accurate measurement.

Calculating H3O+ Concentration from pH

To find the concentration of H3O+ from a given pH, the formula [H3O+] = 10^(-pH) is used. This calculation highlights the relationship between pH and H3O+ concentration, where the number of decimal places in the pH value directly corresponds to the number of significant figures in the calculated concentration. For example, a pH of 2.50 results in a concentration with three significant figures.