Unit consistency check for mass transfer coefficients:\nIdentify the incorrect conversion among the following commonly used unit pairs.

Introduction / Context:
Mass transfer coefficients appear with denominators that mix area and driving-force units (e.g., atm or bar). Converting accurately between SI and English units prevents order-of-magnitude errors in design correlations and vendor data sheets.

Given Data / Assumptions:

• Base conversions: 1 lb = 0.45359237 kg; 1 ft^2 = 0.09290304 m^2; 1 atm = 1.01325 bar.
• Comparisons assume the same driving-force unit (when present) is converted consistently.

Concept / Approach:
For area-only conversions: multiply by (0.45359237 kg/lb) and divide by (0.09290304 m^2/ft^2) to switch from lb/(hr·ft^2) to kg/(hr·m^2). For pressure-unit conversions in denominators, scale numerically by the ratio between atm and bar: value_per_bar = value_per_atm / 1.01325 ≈ 0.98687·value_per_atm.

Step-by-Step Solution:
Convert 1 lb/(hr·ft^2): 0.45359237 / 0.09290304 ≈ 4.8823 kg/(hr·m^2) → option (c) is correct.Inverse relationship: 1 kg/(hr·m^2) should equal about 0.2048 lb/(hr·ft^2), not 4.8823 → option (d) is incorrect.For pressure conversion: 1 kg/(hr·m^2·atm) ≈ 0.98687 kg/(hr·m^2·bar) → option (b) is correct.Option (a) reflects combined area and pressure conversions and is numerically consistent when interpreted with ft^2 (typographical ft^2 vs ft^3 issues aside).

Verification / Alternative check:
Compute the inverse of 4.8823 to confirm ~0.2048, which exposes the error in option (d).

Why Other Options Are Wrong (i.e., not selected):
(a), (b), and (c) are consistent with standard constants; only (d) inverts the area conversion incorrectly.

Common Pitfalls:
Forgetting to invert when switching the direction of conversion; mixing atm↔bar without scaling the numerical value.

Final Answer:
1 kg/(hr·m^2) = 4.8823 lb/(hr·ft^2) is the incorrect conversion.