Water at 500 °C and 250 atm is a supercritical fluid. Under these conditions, Kw is approximately 1.7 * 10^-19. Estimate [H3O+] and [OH-] at 500 °C. Is the water acidic, basic, or neutral?

Verified step by step guidance

Step 1: Understand the concept of the ion product of water (Kw). Kw is the equilibrium constant for the self-ionization of water, given by the expression Kw = [H3O+][OH-]. At 25 °C, Kw is 1.0 x 10^-14, but it changes with temperature.

Step 2: Recognize that at 500 °C, Kw is given as 1.7 x 10^-19. This means that the product of the concentrations of hydronium ions [H3O+] and hydroxide ions [OH-] is 1.7 x 10^-19.

Step 3: Assume that the concentrations of [H3O+] and [OH-] are equal in pure water, as water is neutral. Let [H3O+] = [OH-] = x.

Step 4: Substitute x for both [H3O+] and [OH-] in the expression for Kw: (x)(x) = 1.7 x 10^-19. This simplifies to x^2 = 1.7 x 10^-19.

Step 5: Solve for x by taking the square root of both sides to find the concentration of [H3O+] and [OH-]. Compare the concentrations to determine if the water is acidic, basic, or neutral.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Supercritical Fluids

Supercritical fluids occur when a substance is above its critical temperature and pressure, leading to unique properties that differ from those of gases and liquids. In this state, the fluid can diffuse through solids like a gas and dissolve materials like a liquid, which is significant in understanding the behavior of water at high temperatures and pressures.

Ion Product of Water (Kw)

Kw, the ion product of water, is the equilibrium constant for the self-ionization of water, represented as Kw = [H3O+][OH-]. At different temperatures, Kw varies; at 25 °C, it is 1.0 x 10^-14, but at 500 °C, it increases to approximately 1.7 x 10^-19, indicating a higher concentration of ions in supercritical water, which affects its acidity or basicity.

Acidity and Basicity

The acidity or basicity of a solution is determined by the concentrations of hydronium ions [H3O+] and hydroxide ions [OH-]. A neutral solution has equal concentrations of both ions, while an acidic solution has a higher concentration of [H3O+], and a basic solution has a higher concentration of [OH-]. By calculating [H3O+] and [OH-] from Kw, one can determine the nature of the water at 500 °C.

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