Question

What is the pH of a solution in which [OH- \(]\) equals \(6.9 \times 10^{-10} \mathrm{M} ?\)

Short answer

pH = 4.84

Step-by-step solution

- Understand the relationship between pH and pOH

The pH and pOH of a solution are related by the equation: \[ pH + pOH = 14 \].

- Calculate the pOH

pOH is calculated using the concentration of hydroxide ions \[ OH^- \], given by the formula: \[ pOH = -\text{log}([OH^-]) \]. Substitute the given \[ OH^- \] concentration into the formula:\[ pOH = -\text{log}(6.9 \times 10^{-10}) \].

- Solve for pOH

Calculate the logarithm: \[ pOH = -\text{log}(6.9 \times 10^{-10}) = 9.16 \].

- Calculate the pH

Use the relationship between pH and pOH: \[ pH + pOH = 14 \]. Substitute the value of pOH: \[ pH + 9.16 = 14 \].

- Solve for pH

Isolate pH: \[ pH = 14 - 9.16 \]. Calculate the subtraction: \[ pH = 4.84 \].

Key concepts

pOH

The term pOH refers to the power or potential of hydroxide ions in a solution. It's similar to pH but specifically measures how basic a solution is based on its hydroxide ion concentration. The formula to calculate pOH is \[-\log([OH^-])\]. This calculation uses the concentration of hydroxide ions (OH-) and finds its negative logarithm. Just like the pH scale, pOH values range from 0 to 14. A lower pOH indicates a higher concentration of hydroxide ions, making the solution more basic.

hydroxide ion concentration

The concentration of hydroxide ions in a solution, represented as [OH-], is crucial for understanding its basicity. The concentration is typically measured in moles per liter (M). This value determines both the pOH and the pH of the solution, through the respective formulas. In our exercise, the hydroxide ion concentration is \(6.9 \times 10^{-10} M\), a very low value, indicating a less basic solution. This low concentration leads to a higher pOH, and subsequently, a lower pH when calculated correctly.

logarithmic calculations

Logarithmic calculations are vital in chemistry, especially for finding pH and pOH values. The logarithm (log) function helps convert the wide range of ion concentrations into a more manageable scale. For hydroxide ions, the pOH is calculated using the formula \-log([OH^-])\. In our case, with [OH-] = \(6.9 \times 10^{-10} M\), you calculate \(-\log(6.9 \times 10^{-10})\) to get a pOH of 9.16. Ensure to handle the exponent and mantissa in the scientific notation properly during the log calculation.

acid-base chemistry

Acid-base chemistry involves understanding the balance between hydrogen ions (H+) and hydroxide ions (OH-) in a solution. The pH scale indicates how acidic or basic a solution is, while pOH indicates its basicity. Both pH and pOH scales range from 0 to 14, and together they sum to 14: \[ pH + pOH = 14 \]. Acids have higher concentrations of H+ ions and lower pH values, while bases have higher concentrations of OH- ions and higher pOH values. In our exercise, once we know the pOH, we use the relationship between pH and pOH to find the pH value. This balance is foundational to understanding the behavior of acids and bases in various solutions.