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When glucose (a simple sugar with the chemical formula \(\mathrm{C}_{6}\mathrm{H}_{12}\mathrm{O}_{6}\)) is dissolved in water, it undergoes a process called dissolution. In dissolution, the glucose molecules become evenly distributed among the water molecules, resulting in a homogeneous solution. Water is often referred to as a 'universal solvent', due to its ability to dissolve a wide range of substances, including glucose.
This ability primarily stems from water molecules' polarity, allowing them to interact closely with glucose molecules, aiding the dissolution process.
The solubility of a substance like glucose indicates the maximum amount of it that can be fully dissolved in a specific amount of solvent, often expressed as grams per 100 mL of water. In the case at hand, glucose has a solubility of 120.3 grams per 100 mL. The term 'solubility' is crucial in chemistry to predict how substances will interact in a solution, providing guidance for mixing substances in practical applications.

Proportional calculations are a fundamental mathematical concept used to determine how one quantity relates to another based on a constant ratio. In the context of solubility, these calculations help us find out how much of a solute (in this case, glucose) will dissolve in a different volume of solvent, given its known solubility at a standard volume.
We set up a proportion using the relationship:

• Given solubility: \( \frac{120.3 \, \text{g}}{100 \, \text{mL}} \)
• Desired amount of solvent: \(75.0 \, \text{mL}\)

The setup becomes a mathematical equation where we cross-multiply to find the unknown mass of glucose (\( x \)):
\[ \frac{120.3}{100} = \frac{x}{75.0} \]
This results in the equation:
\[ 120.3 \times 75.0 = 100 \times x \]

Upon solving, we determine the mass of glucose that can be dissolved in the specified arbitrary volume of water. This type of calculation is invaluable, allowing scientists and students alike to make quick and accurate predictions in chemistry based on straightforward arithmetic principles.

Significant figures are the digits in a number that carry meaningful information regarding its precision. In the contexts of scientific measurements, it is crucial to employ significant figures as they convey the accuracy of calculated values based on the inputs used. While doing calculations, we often have to round figures to match the number of significant figures that are meaningful in the context of the problem statement.
For example, when calculating the mass of glucose that can dissolve, the solubility given (120.3 g/100 mL) and volume (75.0 mL) both have four significant figures. Thus, our final result (90.225 g) must be rounded to the same number of significant figures, resulting in 90.2 g.

• This ensures the result retains the correct precision consistent with the initial data's precision.
• Proper use of significant figures avoids overrepresentation or underrepresentation of the accuracy of a given measurement.

Understanding and applying the rule of significant figures is key to delivering precise and reliable scientific communication, especially when the derived results are relied upon for further calculations or practical applications.