Autoionization of water and temperature effect: As the temperature of pure water increases, how do pH and pOH change?

Introduction / Context:Students often memorize pH = 7 for pure water, but this value applies strictly at 25 °C. The ionic product of water, Kw, is temperature dependent. Understanding how pH and pOH vary with temperature is essential for accurate acid–base calculations and water chemistry control.

Given Data / Assumptions:

• Pure water, no added acid or base.
• As temperature increases above 25 °C, Kw increases.
• In pure water: [H+] = [OH−] = (Kw)^0.5 at any temperature.

Concept / Approach:If Kw increases with temperature, both [H+] and [OH−] increase equally in pure water. Because pH = −log10[H+] and pOH = −log10[OH−], increases in concentrations lead to decreases in pH and pOH simultaneously. Neutrality still holds when [H+] = [OH−], but the neutral pH shifts below 7 as temperature rises.

Step-by-Step Solution:

Verification / Alternative check:Pick Kw = 5.5e−14: [H+] = [OH−] = sqrt(5.5e−14) ≈ 7.4e−7 M; pH ≈ 6.13 and pOH ≈ 6.13. Both are less than 7, confirming the trend.

Why Other Options Are Wrong:

• (a), (d) suggest one rises while the other falls, which contradicts equal increases in [H+] and [OH−].
• (c) suggests both increase; they actually decrease as concentrations increase.
• (e) fixes pH at 7 regardless of temperature, which is false.

Common Pitfalls:Believing “neutral = pH 7” at all temperatures; neglecting Kw’s temperature dependence in reactor, boiler, or cooling-water calculations.

Final Answer:pOH and pH both decrease