Baumé gravity scale (heavy liquids):\nWhich expression defines degrees Baumé (°Bé) for liquids heavier than water in terms of specific gravity G (at the reference temperature)?

Difficulty: Easy

Correct Answer: 145 - (145 / G)

Explanation:


Introduction / Context:
The Baumé scale is a hydrometer scale historically used in chemical processing to express the density of liquids. Different formulas exist for liquids lighter or heavier than water. Correctly identifying the relation prevents miscalculation of concentrations, especially in legacy specifications and plant procedures.


Given Data / Assumptions:

  • G denotes specific gravity (dimensionless) at the reference temperature.
  • We require the expression applicable to heavy liquids (G > 1).
  • Standard Baumé convention is assumed.


Concept / Approach:
For liquids heavier than water, the Baumé degrees decrease as specific gravity increases. The conventional formula is °Bé = 145 − 145/G (at 60°F reference in common U.S. practice). For liquids lighter than water, a different formula is used. Note that API gravity and other scales have different constants and should not be confused with Baumé.


Step-by-Step Solution:

Identify the correct heavy-liquid relation: °Bé = 145 − (145 / G).Verify dimensionality: G is unitless; °Bé is by definition in degrees Baumé.Reject alternate constants that belong to other scales (e.g., API).


Verification / Alternative check:
Handbooks list the complementary light-liquid formula as °Bé = 140/G − 130, emphasizing that constants differ by convention and reference temperature.


Why Other Options Are Wrong:

  • (141.5/G) − 131.5: that is the API gravity relationship, not Baumé.
  • 200(G − 1) and (400/G) − 400: not standard Baumé definitions.
  • 100(1 − 1/G): an ad hoc expression lacking Baumé foundations.


Common Pitfalls:
Using the light-liquid formula for heavy liquids; always check whether G is above or below 1 and apply the corresponding equation.


Final Answer:
145 - (145 / G).

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