Baumé gravity scale (liquids lighter than water): Select the correct defining equation for °Bé when specific gravity G < 1.

Introduction / Context:The Baumé (°Bé) hydrometer scale predates API gravity and remains in use for some process liquids. Two distinct definitions exist: one for liquids lighter than water and another for heavier liquids. Correctly identifying the formula matters when converting between °Bé and specific gravity G for sizing, blending, or quality control.

Given Data / Assumptions:

• G denotes specific gravity referenced to water at standard conditions.
• Different constants apply for lighter vs. heavier than water.
• We focus on the “lighter than water” case (G < 1).

Concept / Approach:Historical definitions of the Baumé scale commonly used are:• For liquids lighter than water: °Bé = (140 / G) − 130.• For liquids heavier than water: °Bé = 145 − (145 / G).The constants reflect calibration of the original hydrometers and are empirical; modern practice often prefers API gravity for petroleum, but Baumé remains relevant in various industries.

Step-by-Step Reasoning:

Verification / Alternative check:If G = 1.0 (water), the lighter-than-water formula yields °Bé = 10, which aligns with traditional conventions (water near 10 °Bé on the “lighter” scale boundary definitions).

Why Other Options Are Wrong:

• 200(G − 1): Not a standard Baumé relation.
• 145 − (145/G): This is the heavier-than-water relation, not applicable here.
• (400/G) − 400: Non-standard and dimensionally inconsistent with usual constants.

Common Pitfalls:Mixing the lighter/heavier formulas; confusing Baumé with API gravity (API uses 141.5 and 131.5 constants and is defined only for petroleum liquids).

Final Answer:°Bé = (140 / G) − 130