Psychrometrics — percentage humidity from relative humidity:\nAir at 20°C and 750 mm Hg has relative humidity 80%. Given water vapor pressure at 20°C is 17.5 mm Hg, compute the percentage humidity of the air.

Introduction / Context:
Humidity measures are central to drying, HVAC, and gas–liquid mass transfer. While relative humidity (RH) compares the actual partial pressure of water vapor to its saturation value at the same temperature, percentage humidity compares the humidity ratio (water per dry air) to the saturation humidity ratio at the same conditions. The two are not identical because the denominator for humidity ratio includes the dry-air term (P − p_v) rather than the total pressure P.

Given Data / Assumptions:

• Total pressure P = 750 mm Hg.
• Temperature = 20°C; saturation vapor pressure p_vs = 17.5 mm Hg.
• Relative humidity φ = 80% → p_v = 0.80 * p_vs = 14.0 mm Hg.
• Ideal gas behavior; standard psychrometric definitions.

Concept / Approach:
Humidity ratio Y (kg H2O/kg dry air) is proportional to p_v/(P − p_v). At saturation, Y_s ∝ p_vs/(P − p_vs). The percentage humidity is defined as 100 * (Y/Y_s) = 100 * [p_v (P − p_vs)] / [p_vs (P − p_v)].

Step-by-Step Solution:
Compute p_v from RH: p_v = 0.80 * 17.5 = 14.0 mm Hg.Apply formula: % humidity = 100 * [p_v (P − p_vs)] / [p_vs (P − p_v)].Substitute values: numerator = 14.0 * (750 − 17.5) = 14.0 * 732.5 = 10255.0.Denominator = 17.5 * (750 − 14.0) = 17.5 * 736 = 12880.0.Ratio = 10255.0 / 12880.0 = 0.7965 ≈ 79.65% → matches 79.62% within rounding.

Verification / Alternative check:
If we (incorrectly) equate percentage humidity to relative humidity, we would get 80%, which is slightly higher. The small difference arises from the (P − p_v) vs. (P − p_vs) terms in the humidity-ratio definition.

Why Other Options Are Wrong:
80.38 or 78.51: result from arithmetic/rounding errors or misapplied formulas.80: equal to RH, but percentage humidity is not exactly RH except at very low pressures or special limits.

Common Pitfalls:
Confusing RH with percentage humidity; forgetting to use (P − p_v) and (P − p_vs) in the humidity-ratio expressions; mixing absolute/relative units.

Final Answer:
79.62