Degrees Brix (°Bx) for sugar solutions: which of the following formulas defines the Brix scale in terms of specific gravity G?

Introduction / Context:Degrees Brix (°Bx) is a widely used measure in food, beverage, and fermentation industries. It is defined as the mass percentage of sucrose in a sucrose–water solution. While hydrometers or refractometers are often used to estimate °Bx from density or refractive index, the formal definition is not a specific gravity formula but rather a weight percent specification tied to sucrose content.

Given Data / Assumptions:

• G denotes specific gravity at a defined reference temperature.
• Hydrometer scales (e.g., °Baumé, °API) have simple algebraic relations to G.
• Brix is defined as % (w/w) sucrose; empirical correlations to G exist but are not the definition.

Concept / Approach:By definition, 1 °Bx = 1 g sucrose per 100 g solution. Any relationship converting specific gravity to °Bx is an empirical correlation valid over a range and must be referenced to temperature and solution composition (sucrose-only). The choices given match other hydrometer scales: °Baumé for heavy liquids uses 145 − 145/G; °API uses 141.5/G − 131.5; and other linear forms are not the Brix definition. Therefore, none of the listed formulas is the definition of °Bx.

Step-by-Step Solution:

Verification / Alternative check:Industry references define °Bx via sucrose mass fraction; tables and polynomial fits convert G to °Bx, but no single simple linear formula universally defines it across concentrations and temperatures.

Why Other Options Are Wrong:

• (400/G) − 400 and 200(G − 1): not standard definitions for °Bx.
• 145 − (145/G): corresponds to °Baumé for heavy liquids, not °Brix.
• (141.5/G) − 131.5: °API gravity (petroleum), not °Brix.

Common Pitfalls:Assuming °Brix is a hydrometer scale like °Baumé or °API. Remember: °Brix is a composition definition; instruments infer it via correlations from density or refractive index.

Final Answer:none of these