Question

If a neutral solution of water, with \(\mathrm{pH}=7.00\), is heated to \(50^{\circ} \mathrm{C}\), the pH drops to 6.63 . Does this mean that the concentration of \(\left[\mathrm{H}^{+}\right]\) is greater than the concentration of \(\left[\mathrm{OH}^{-}\right] ?\) Explain.

Short answer

Although the pH of the solution drops to 6.63 when heated to 50°C, the pOH increases to 7.37, still maintaining the relationship \(pH + pOH = 14\). Since the pOH is greater than the pH, the concentration of \(\mathrm{OH}^{-}\) ions is greater than the concentration of \(\mathrm{H}^{+}\) ions, and the solution remains neutral.

Step-by-step solution

Understanding pH and pOH

The pH of a solution is a measure of the concentration of hydronium ions (\(\mathrm{H}^{+}\)) in the solution. It is given by the formula: \( \mathrm{pH} = -\log_{10} [\mathrm{H}^{+}] \) Similarly, the pOH of a solution is a measure of the concentration of hydroxide ions (\(\mathrm{OH}^{-}\)) in the solution: \( \mathrm{pOH} = -\log_{10} [\mathrm{OH}^{-}] \) Importantly, the relationship between pH and pOH is given by the following formula: \( \mathrm{pH} + \mathrm{pOH} = 14 \)

Finding the pOH at 25°C

Since the initial pH of the solution is given as 7.00, we can find the pOH at room temperature (25°C) using the formula: \( \mathrm{pOH} = 14 - \mathrm{pH} \) \( \mathrm{pOH} = 14 - 7.00 = 7.00 \) Since pH and pOH are equal, the solution is neutral and the concentrations of \(\mathrm{H}^{+}\) and \(\mathrm{OH}^{-}\) are equal.

Finding the pOH at 50°C

The problem states that when the solution is heated to 50°C, the pH drops to 6.63. We can find the pOH at this temperature using the same formula: \( \mathrm{pOH} = 14 - \mathrm{pH} \) \( \mathrm{pOH} = 14 - 6.63 = 7.37 \)

Comparing the concentrations of H+ and OH- ions at 50°C

With the calculated pOH value, we can now compare the concentrations of \(\mathrm{H}^{+}\) and \(\mathrm{OH}^{-}\) ions at 50°C. If the pOH is greater than the pH, the concentration of \(\mathrm{OH}^{-}\) ions would be greater than the concentration of \(\mathrm{H}^{+}\) ions, meaning that the solution is still neutral. Since the pOH value we calculated at 50°C is 7.37, which is greater than the pH value of 6.63, the concentration of \(\mathrm{OH}^{-}\) ions is indeed greater than the concentration of \(\mathrm{H}^{+}\) ions at this temperature. In conclusion, although the pH of the solution drops when it is heated to 50°C, the concentrations of \(\mathrm{H}^{+}\) ions and \(\mathrm{OH}^{-}\) ions remain equal, and the solution remains neutral.

Key concepts

pH and pOH Relationship

Understanding the relationship between pH (potential of hydrogen) and pOH (potential of hydroxide) is essential when studying aqueous solutions. The pH scale measures how acidic or basic a solution is, with lower values being more acidic and higher values being more basic. The pOH scale, on the other hand, operates similarly but reflects the concentration of hydroxide ions instead.

The pH and pOH of a solution are inversely related and interconnected by the equation: center> \( \mathrm{pH} + \mathrm{pOH} = 14 \) center>This is true for aqueous solutions at 25°C (298 K), and deviations from this standard temperature can cause this relationship to shift slightly. The sum of the pH and pOH gives us the constant value of 14, which is derived from the ion product constant of water at this temperature. It is crucial to recognize that changes in temperature will affect the pH and pOH values independently, and though their sum may differ from 14 at temperatures other than 25°C, the intrinsic relationship remains a powerful tool for understanding solution chemistry.

Hydronium Ion Concentration

The hydronium ion concentration (\([\mathrm{H}^{+}]\)or alternatively \([\mathrm{H}_3\mathrm{O}^{+}]\)) is a critical factor in determining the acidity of a solution. It is expressed using a logarithmic scale known as pH, which stands for 'potential of hydrogen.' The pH of a solution is calculated using the formula:center> \( \mathrm{pH} = -\log_{10} [\mathrm{H}^{+}] \)center>A neutral solution, such as pure water, at 25°C has a pH of 7. As temperature rises, the tendency for water molecules to dissociate into hydronium and hydroxide ions increases, resulting in a change in pH. However, while the pH may change, this does not necessarily mean that the solution becomes more acidic or basic; it may simply reflect the shift in equilibrium due to temperature changes. Therefore, a careful analysis of both pH and pOH is required to fully understand the effects of temperature on hydronium ion concentration.

Hydroxide Ion Concentration

The concentration of hydroxide ions (\([\mathrm{OH}^{-}]\)) is another fundamental aspect when analyzing the nature of solutions. It is quantified by the pOH value, given by:center> \( \mathrm{pOH} = -\log_{10} [\mathrm{OH}^{-}] \)center>Understanding the hydroxide ion concentration is crucial when dealing with solutions' basicity, with higher pOH indicating lower concentrations of \([\mathrm{OH}^{-}]\)and thus less basic solutions. Similar to hydronium ions, the behavior of hydroxide ions is influenced by temperature. An increase in temperature generally results in an increased disassociation of water molecules, affecting the concentration of hydroxide ions in the process. Consequently, the pOH will change with temperature in a predictable manner, as it is closely tied to the disassociation constant of water, which is temperature-dependent.

Neutral Solution

A neutral solution is characterized by having an equal concentration of hydronium ions (\([\mathrm{H}^{+}]\)) and hydroxide ions (\([\mathrm{OH}^{-}]\)). At a standard temperature of 25°C (298 K), this condition is met when the pH and pOH both equal 7, resulting in a pH of exactly 7.

However, when the temperature changes, so does the equilibrium between hydronium and hydroxide ions. At higher temperatures, water molecules are more likely to dissociate, which can affect the pH value without necessarily disturbing the neutral state of the solution. This means that the pH of a neutral solution may change with temperature, but as long as the ratio of \([\mathrm{H}^{+}]\)to \([\mathrm{OH}^{-}]\)remains equal, the solution is still considered neutral. For example, at 50°C, the pH may drop below 7, but if the decrease in pH is matched by a corresponding increase in pOH, the neutral character of the water remains intact. This is a crucial concept, as it emphasizes that neutrality is not solely dependent on a pH of 7 but rather on the balance of hydronium and hydroxide ion concentrations.