Questions: Calculate the H^+ ion concentration in a solution with a pH of 3.85.
Transcript text: Calculate the $\mathrm{H}^{+}$ ion concentration in a solution with a pH of 3.85.
Solution
Solution Steps
Step 1: Understanding the Relationship Between pH and \(\mathrm{H}^{+}\) Ion Concentration
The pH of a solution is defined as the negative logarithm (base 10) of the hydrogen ion concentration. Mathematically, this is expressed as:
\[
\text{pH} = -\log_{10}[\mathrm{H}^{+}]
\]
Step 2: Rearranging the Formula to Solve for \([\mathrm{H}^{+}]\)
To find the \(\mathrm{H}^{+}\) ion concentration, we need to rearrange the formula:
\[
[\mathrm{H}^{+}] = 10^{-\text{pH}}
\]
Step 3: Substituting the Given pH Value
Substitute the given pH value of 3.85 into the formula:
\[
[\mathrm{H}^{+}] = 10^{-3.85}
\]
Step 4: Calculating the \(\mathrm{H}^{+}\) Ion Concentration
Calculate the \(\mathrm{H}^{+}\) ion concentration using the expression:
\[
[\mathrm{H}^{+}] = 10^{-3.85} \approx 1.413 \times 10^{-4}
\]
Final Answer
The \(\mathrm{H}^{+}\) ion concentration in the solution is \(\boxed{1.413 \times 10^{-4}}\).