Questions: The pH scale is a way to quantify the acidity or basicity of a solution. The pH of a solution depends upon the concentration of hydronium ion, [H3O+], in that solution. The relationship between pH and hydronium ion concentration (in units of molarity, M) may be expressed as: - pH = log [H3O+] If the pH of 250.0 mL of a certain solution is found to be 3.27, what is the hydronium ion concentration in the solution?

The pH scale is a way to quantify the acidity or basicity of a solution. The pH of a solution depends upon the concentration of hydronium ion, [H3O+], in that solution. The relationship between pH and hydronium ion concentration (in units of molarity, M) may be expressed as: - pH = log [H3O+] If the pH of 250.0 mL of a certain solution is found to be 3.27, what is the hydronium ion concentration in the solution?
Transcript text: The pH scale is a way to quantify the acidity or basicity of a solution. The pH of a solution depends upon the concentration of hydronium ion, $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$, in that solution. The relationship between pH and hydronium ion concentration (in units of molarity, M) may be expressed as: \[ -\mathrm{pH}=\log \left[\mathrm{H}_{3} \mathrm{O}^{+}\right] \] If the pH of 250.0 mL of a certain solution is found to be 3.27 , what is the hydronium ion concentration in the solution?
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Solution

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Solution Steps

Step 1: Understanding the Relationship Between pH and Hydronium Ion Concentration

The relationship between pH and the concentration of hydronium ions, \([\mathrm{H}_3\mathrm{O}^+]\), is given by the equation: \[ \mathrm{pH} = -\log \left[\mathrm{H}_3\mathrm{O}^+\right] \]

Step 2: Rearranging the Equation to Solve for \([\mathrm{H}_3\mathrm{O}^+]\)

To find the hydronium ion concentration, we need to rearrange the equation: \[ \left[\mathrm{H}_3\mathrm{O}^+\right] = 10^{-\mathrm{pH}} \]

Step 3: Substituting the Given pH Value

Given that the pH of the solution is 3.27, we substitute this value into the equation: \[ \left[\mathrm{H}_3\mathrm{O}^+\right] = 10^{-3.27} \]

Step 4: Calculating the Hydronium Ion Concentration

Using a calculator to find \(10^{-3.27}\): \[ \left[\mathrm{H}_3\mathrm{O}^+\right] \approx 5.3703 \times 10^{-4} \, \text{M} \]

Final Answer

\[ \boxed{\left[\mathrm{H}_3\mathrm{O}^+\right] = 5.3703 \times 10^{-4} \, \text{M}} \]

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