How many moles of glucose are there in \(255.0 \mathrm{~mL}\) of a \(0.998 \mathrm{M}\) solution of glucose?

Understanding how to calculate the number of moles of a solute in a solution is a fundamental concept in chemistry. A mole is a unit of measurement used to express amounts of a chemical substance, and it is defined as the amount of substance that contains as many entities (such as atoms, molecules, ions, etc.) as there are atoms in 12 grams of pure carbon-12.
When dealing with solutions, the solute is the substance dissolved in a solvent to form the solution. The concentration of a solute in a solution is often given in terms of molarity (M), which is the number of moles of solute per liter of solution.
To find the moles of solute, you multiply the molarity by the volume of the solution in liters. For instance, if you have a 0.998 M glucose solution, and you want to know the amount of moles in 0.255 liters of this solution, you simply perform the multiplication:

• \( 0.998 \text{ moles/L} \) (the concentration) times
• \( 0.255 L \) (the volume of the solution) equals
• \( 0.25449 \text{ moles} \) of glucose.

Making sure to align this calculation with significant figures ensures the accuracy and precision of your result.

In chemistry and laboratory practices, volume conversion is an essential skill. Volumes can be expressed in multiple units, such as liters (L), milliliters (mL), cubic centimeters (cc or cm³), and more. To work with molarity, which is moles per liter, you typically need to convert your volume to liters if it's given in another unit.
Converting milliliters to liters is a straightforward process because the metric system is based on powers of ten. Since one liter is equal to 1000 milliliters, you convert by dividing the number of milliliters by 1000. For example:

• \( 255.0 \text{ mL} \) is equal to
• \( 255.0 \times \frac{1 L}{1000 mL} = 0.255 L \).

This step is crucial because using the correct volume unit in calculations affects the final outcome significantly.

The concept of significant figures relates to the precision of measurements and calculations in science. When you measure or calculate something, the number of significant figures is the number of digits believed to be correct by the person doing the measurement. It includes all the certain digits and the first uncertain digit.
In a sense, significant figures communicate the precision of a measurement. In calculations, the rule of thumb is that your final answer should not have more significant figures than the measurement with the least number of significant figures. For instance, when multiplying 0.255 L (which has four significant figures) by 0.998 M (which has three significant figures), your answer should be rounded to three significant figures, thus \( 0.25449 \text{ moles} \) gets rounded to \( 0.254 \text{ moles} \). This step ensures that the inherent precision (or lack thereof) in the measurements is respected in the final answer and doesn't erroneously imply a greater degree of precision than what is actually present.