Question

What is the pH of a neutral solution at a temperature when Kw = 1.8 × 10^-14? Option 1: pH 7 Option 2: pH 1 Option 3: pH 14 Option 4: pH 0

Answer 1

The pH of a neutral solution when Kw = 1.8 ×
`10^{-14` is 6.87, as the pKw is 13.74 and for a neutral solution, the pH is half of the pKw. None of the options provided are correct, but the closest is Option 1: pH 7, which is for a different temperature.

Step-by-step explanation:

The pH of a neutral solution at a temperature when Kw = 1.8 ×
`10^{-14` can be determined by understanding that pH is defined as the negative logarithm of the hydrogen ion concentration ([H+]), while pOH is defined as the negative logarithm of the hydroxide ion concentration ([OH-]). For a solution to be neutral, [H+] must equal [OH-], meaning the solution has equal concentrations of hydrogen and hydroxide ions. Given that pKw = pH + pOH, we can calculate the pH of the neutral solution.

Since pKw = -log(Kw), for Kw = 1.8 ×
`10^{-14`, pKw is calculated as -log(1.8 × 10-14) = 13.74. For a neutral solution, pH = pOH, so pH is half of pKw. Therefore, pH = 13.74 / 2 = 6.87. So, the correct option is none of the provided choices, but the closest answer would be Option 1: pH 7, which is the pH of a neutral solution at 25 °C. However, it is crucial to remember that pH varies with temperature and the pH of a neutral solution changes correspondingly.