Questions: Given a watery solution in which 1 / 1,000,000(1 × 10^-6) particles are free H+ ions, what will the pH be?

Transcript text: Given a watery solution in which $1 / 1,000,000\left(1 \times 10^{-6}\right)$ particles are free $\mathrm{H}^{+}$ions, what will the pH be?

Solution

Solution Steps

Step 1: Understanding the pH Formula

The pH of a solution is calculated using the formula: \[ \text{pH} = -\log_{10}[\text{H}^+] \] where $[\text{H}^+]$ is the concentration of hydrogen ions in moles per liter.

Step 2: Identify the Concentration of $\text{H}^+$ Ions

The problem states that the concentration of $\text{H}^+$ ions is $1 \times 10^{-6}$ moles per liter.

Step 3: Calculate the pH

Substitute the concentration into the pH formula: \[ \text{pH} = -\log_{10}(1 \times 10^{-6}) \] Using the properties of logarithms, we know: \[ -\log_{10}(1 \times 10^{-6}) = -(-6) = 6 \]

Final Answer

The pH of the solution is $\boxed{6}$.

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