Question

The \(\mathrm{pH}\) of a solution is decreased by one unit. The hydrogen ion concentration is increased by what factor?

Short answer

If the pH of a solution decreases by one unit, the hydrogen ion concentration increases by a factor of 10.

Step-by-step solution

Understand the relationship between pH and Hydrogen ion concentration

The relationship between pH and Hydrogen ion concentration is given by the formula, pH = -log[H+]. It is important to understand that a decrease in pH indicates an increase in Hydrogen ion concentration.

Calculate the change in Hydrogen ion concentration

If the pH decreases by one unit, due to the logarithmic nature of the pH scale - which is base 10 - the Hydrogen ion concentration increases by a factor of 10.

Formulate the conclusion

As such, a decrease in pH by one unit results in a tenfold increase in the hydrogen ion concentration.

Key concepts

Logarithmic pH Scale

The pH scale is a convenient way to represent the acidity or basicity of a solution. Defined as the negative logarithm of the hydrogen ion concentration, the pH scale is logarithmic, meaning each unit change represents a tenfold change in concentration. So, when you hear that a solution's pH has dropped or risen by one unit, it's important to understand that this is not a linear change. A decrease by one unit actually means the concentration of hydrogen ions has increased by ten times, and an increase by one unit means hydrogen ions have decreased by a factor of ten. This logarithmic nature allows the pH scale to comfortably span the wide range of hydrogen ion concentrations found in various substances, from battery acid to hand soap to pure water.

Hydrogen Ion Concentration

Our next stop is the hydrogen ion concentration itself, typically denoted by \[H^+\] or \[H_3O^+\] for the hydronium ion. This concentration directly dictates the acidity or basicity of a solution. For a more intuitive grasp, think of these ions as 'spicy' particles: more of them means a spicier (more acidic) taste on the pH flavor scale. This varies from less than one ten-millionth of a gram per liter for pure water to much higher concentrations in acidic solutions. It's critical to understand that small numerical changes can indicate large shifts in concentration due to the logarithmic scale, enhancing the impact of these 'flavorful' ions on a solution's overall character.

pH Scale and Concentration Relationship

Delving deeper into the pH scale and concentration relationship, it becomes clear how intertwined they are. The equation pH = -log[\[H^+\]] embodies their inverse relationship. As the concentration of hydrogen ions ([\[H^+\]]) increases, the log of this concentration increases, resulting in a larger negative value when you apply the negative sign in the equation. As a result, the pH value decreases. So, when the exercise mentions a decrease in pH by one unit, we can conclude that the hydrogen ion concentration has not just increased but increased tenfold. This leads to noticeable changes in the solution's properties. For example, a neutral solution with a pH of 7 that decreases to a pH of 6 becomes ten times more acidic.

Acid and Base Chemistry

Last but certainly not least is acid and base chemistry, encapsulated by the dance of hydrogen ions and hydroxide ions in solution. Acids are generous donors of hydrogen ions, adding 'spice' to the solution, while bases do the opposite by accepting hydrogen ions, reducing the 'spiciness'. The strength of an acid or base is measured in part by its ability to alter the hydrogen ion concentration in a solution. This is why monitoring pH is crucial in chemical experiments, industrial processes, and even the human body. It's a delicate balance that can tip a solution's identity from one that nurtures life to one that corrodes metal.