Question

The two molecular scenes below depict the relative concentrations of (purple) in solutions of the same volume (with counter ions and solvent molecules omitted for clarity). If the pH in scene A is 4.8, what is the pH in scene B?

Short answer

The pH in scene B is $\text{pH=3.70}$.

Step-by-step solution

Concept Introduction

An acid is a type of chemical that produces sour solutions due to a high concentration of positive hydrogen ions in the solution.

A base is a type of chemical that produces bitter-tasting solutions due to a lack of positive hydrogen ions. Acids and bases combine to generate salts.

The term "neutral" refers to a substance that is in the middle of the acid-base spectrum.

What is the pH in scene B ?

Let's start by figuring out how many moles (n) each purple molecule is. First, solve for $\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]$in scene A.

$\begin{array}{c}\text{pH=-log}\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]\\ \left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]{\text{=10}}^{\text{-pH}}\\ {\text{=10}}^{\text{-4.8}}\\ \left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]{\text{=1.58×10}}^{\text{-5}}\text{M}\end{array}$

We can assume the volume is 1 and the concentration = moles for A because the volume in scenes and B are the same. To get the amount of moles per purple molecule, divide the moles by two.

${\text{1.58×10}}^{\text{-5}}{\text{mol÷2molecule=7.92×10}}^{\text{-6}}\frac{\text{mol}}{\text{molecule}}$