- Start with the definition: \(pH = -\log_{10} [H^+]\).
- Substitute the given pH value: \(7.2 = -\log_{10} [H^+]\).
- Rearrange to isolate the log term: \(\log_{10} [H^+] = -7.2\).
- Convert to exponential form to find the final expression: \([H^+] = 10^{-7.2}\), which corresponds to option a.
- The final answer is \(\boxed{a}\).
Explanation
- Analyzing the Problem Definition
The problem defines the pH of a substance as \[pH = -\log_{10} [H^+]\] where \([H^+]\) represents the concentration of hydrogen ions. We are given a solution with a pH of 7.2 and need to determine the correct equation that expresses \([H^+]\) in terms of this value. This requires isolating \([H^+]\) within the logarithmic equation.
- Setting up the Equation
Given that the pH is 7.2, we substitute this into the formula: \[7.2 = -\log_{10} [H^+]\]
To isolate the logarithmic term, we multiply both sides of the equation by \(-1\):
\[-7.2 = \log_{10} [H^+]\]
- Solving for [H^+] and Matching Options
The definition of a logarithm states that if \(\log_b(x) = y\), then the equivalent exponential form is \(x = b^y\). Applying this to our equation where the base \(b\) is 10, \(x\) is \([H^+]\), and \(y\) is \(-7.2\), we obtain:
\[[H^+] = 10^{-7.2}\]
Comparing this result to the given options, we see that it matches option a.
Examples
In chemistry and biology, the concentration of hydrogen ions in a solution is crucial for understanding its acidity or alkalinity. For instance, blood typically has a pH around 7.4. By using the inverse relationship between pH and hydrogen ion concentration, scientists can precisely calculate the molarity of ions present. This helps in maintaining homeostasis in biological systems or monitoring chemical reactions in industrial processes where precise pH control is required. Understanding this conversion is a fundamental skill for interpreting scientific data.