Question

Water superheated under pressure to \(200^{\circ} \mathrm{C}\) and \(750 \mathrm{~atm}\) has \(K_{w}=1.5 \times 10^{-11}\). What is \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\) at \(200^{\circ} \mathrm{C}\) ? Is the water acidic, basic, or neutral?

Short answer

\([\mathrm{H}_{3}\mathrm{O}^{+}] = [\mathrm{OH}^{-}] \approx 3.87 \times 10^{-6}\); neutral.

Step-by-step solution

Identify the given information

The temperature of the water is \(200^{\circ} \mathrm{C}\) and the pressure is \(750 \mathrm{~atm}\). The ion product of water is given as \(K_{w}=1.5 \times 10^{-11}\).

Understand the relationship between hydronium and hydroxide ion concentrations

The ion product of water \(K_w\) is defined as the product of the concentrations of hydronium ions and hydroxide ions in water: \[ K_w = [\mathrm{H}_{3}\mathrm{O}^{+}][\mathrm{OH}^{-}] \] Since it's pure water, we can assume \([\mathrm{H}_{3}\mathrm{O}^{+}] = [\mathrm{OH}^{-}]\).

Set up the equation

Since \([\mathrm{H}_{3}\mathrm{O}^{+}] = [\mathrm{OH}^{-}] = x\), we substitute into the equation: \[ x^2 = 1.5 \times 10^{-11} \]

Solve for x

Take the square root of both sides to find \(x\), which represents both \([\mathrm{H}_{3}\mathrm{O}^{+}]\) and \([\mathrm{OH}^{-}]\): \[ x = \sqrt{1.5 \times 10^{-11}} \] \[ x \approx 3.87 \times 10^{-6} \]

Assess whether the solution is acidic, basic, or neutral

Since \([\mathrm{H}_{3}\mathrm{O}^{+}] = [\mathrm{OH}^{-}]\), the solution is neutral at this temperature.

Key concepts

Hydronium ion concentration

Hydronium ions, represented as \(\mathrm{H}_3\mathrm{O}^+\), are a central component in understanding acidity in solutions. In water at any temperature, the concentration of hydronium ions helps determine if the water is acidic, neutral, or basic.

When dealing with water at higher temperatures, like \(200^{\circ} \mathrm{C}\), it's essential to account for the ion product of water, \(K_w\). This product equates to the multiplication of hydronium and hydroxide ion concentrations.

• For equilibrium in water: \[ K_w = [\mathrm{H}_3\mathrm{O}^+][\mathrm{OH}^-] \]
• At \(200^{\circ} \mathrm{C}\), \(K_w\) is altered compared to standard conditions.

Thus, understanding hydronium ions at superheated temperatures involves solving for their concentration using the updated \(K_w\).

Hydroxide ion concentration

Hydroxide ions, denoted as \(\mathrm{OH}^-\), work alongside hydronium ions to maintain the balance described by the ion product of water.

Under normal conditions at \(25^{\circ} \mathrm{C}\), water has a \(K_w\) value of \(1 \times 10^{-14}\), but at \(200^{\circ} \mathrm{C}\) and 750 atm, this value shifts to \(1.5 \times 10^{-11}\). Calculating \(\mathrm{OH}^-\) concentration requires solving the equation:

• If \([\mathrm{H}_3\mathrm{O}^+] = [\mathrm{OH}^-]\), then: \[x^2 = 1.5 \times 10^{-11}\]
• Solving provides \(x \approx 3.87 \times 10^{-6}\).

This change reflects the dynamic nature of water's equilibrium and highlights the impact of temperature on ion concentrations.

Water neutrality

Water neutrality refers to a balance where the concentration of hydronium ions equals that of hydroxide ions.

At \(200^{\circ} \mathrm{C}\), this balance is maintained even with a different \(K_w\) value. In our example:

• We found both \([\mathrm{H}_3\mathrm{O}^+]\) and \([\mathrm{OH}^-]\) to be approximately \(3.87 \times 10^{-6}\).
• Since these concentrations are equal, the water remains neutral.

Neutrality at such high temperatures shows that the water isn’t acidic or basic under these conditions, even though individual ion concentrations might appear different from those at room temperature.

Superheated water

Superheated water is water heated above its boiling point under pressure, allowing it to remain liquid.

For instance, at \(200^{\circ} \mathrm{C}\) and 750 atm, water doesn’t boil, but its chemical properties change.

• The ion product \(K_w\) is significantly different from normal temperature \(K_w\), illustrating temperature and pressure effects.
• This can affect calculations of both \(\mathrm{H}_3\mathrm{O}^+\) and \(\mathrm{OH}^-\).

Understanding superheated water is vital in contexts like industrial applications, where precise chemical properties are crucial for processes.