Final answer:
To determine the pH of a solution with 5.3 × 10¹⁷ OH⁻ ions per liter, calculate the pOH by taking the negative logarithm of the hydroxide ion concentration, and then subtract that from 14 to find the pH.
Step-by-step explanation:
The question asks, "What is the pH of an aqueous solution that contains 5.3 × 10¹⁷ OH⁻ ions per liter of solution?" To find the pH, we first need to calculate the pOH using the given hydroxide ion concentration. The pOH can be found by taking the negative logarithm (base 10) of the hydroxide ion concentration. The formula for pOH is:
pOH = -log[OH⁻]
We are then given the concentration of hydroxide ions to be 5.3 × 10¹⁷ M. Inserting this value into the pOH formula:
pOH = -log(5.3 × 10¹⁷ M)
This calculation yields a pOH value. After calculating pOH, we can find the pH by using the relation that pH + pOH = 14.00 at 25°C.
pH = 14.00 - pOH
By subtracting the calculated pOH from 14.00, we get the pH of the solution. The pH indicates whether the solution is acidic, basic, or neutral. The pH value will also indicate that the solution is basic as it has a concentration of hydroxide ions higher than that of a neutral solution, which is 1.0 × 10⁻⁷ M.
Finally, the result would have two significant figures to match the given data. Understanding the logarithmic nature of pH, which condenses the range of hydrogen ion concentrations into manageable numbers, is crucial. This example showcases how a small difference in pH is indicative of a large difference in hydrogen ion concentration.