A flask containing \(9.55 \mathrm{~mL}\) of a liquid weighs \(157.2 \mathrm{~g}\) with the liquid in the flask and \(148.4 \mathrm{~g}\) when empty. Calculate the density of the liquid in \(\mathrm{g} / \mathrm{mL}\) to the correct number of significant digits.

Understanding the concepts of mass and volume is crucial in the world of chemistry, especially when calculating the density of a substance. Mass refers to the amount of matter an object contains, while volume is the space that matter occupies. In the given exercise, the mass is measured in grams (g) and the volume in milliliters (mL), which are common units in chemistry for these measurements.

To accurately determine the mass of the liquid in the flask, one must weigh the flask with and without the liquid, then subtract the mass of the empty flask from the mass of the flask with the liquid. This step is fundamental because any errors in mass measurement will directly affect the density calculation. Volume measurements, typically less prone to error if a properly calibrated container is used, must also be precise. In the exercise, the volume is given as 9.55 mL, and this precision indicates confidence in the volume measurement.

Accuracy in mass and volume measurements is not only essential for finding density, but also for other laboratory procedures, making these concepts foundational in chemistry.

Significant figures are a critical component of measurements in chemistry, reflecting the precision of those measurements. They show us the degree of uncertainty in the last digit of any given number. The rule is that the final result should be reported with the same number of significant figures as the measurement with the least number of significant figures.

In our exercise, we notice that the given mass measurements (157.2 g and 148.4 g) each have four significant figures, while the volume measurement (9.55 mL) has three significant figures. This means that our final answer for density should be reported with three significant figures, as it is the smallest number of significant figures from our measurements.

It is important to consistently apply the rules of significant figures in all steps of a calculation. For example, when calculating the mass of the liquid by subtracting the mass of the empty flask from the total mass, the result should also be reported in accordance with the rules of significant figures.

The density of a material can be thought of as its 'compactness' or how much mass is contained within a certain volume. To find the density, we use a straightforward formula: \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \).

Here, the density will have the units of the mass divided by the volume, often expressed in grams per milliliter (\(\text{g/mL}\)) in chemistry. After determining the mass of the liquid by subtracting the weight of the empty flask from the weight of the flask with the liquid, we use this formula to calculate the liquid's density using the volume provided.

For our specific exercise, the mass of the liquid was found to be 8.8 g (157.2 g - 148.4 g = 8.8 g). By using the given volume of 9.55 mL, the density is then calculated to be 0.921 g/mL. This value, when properly rounded to three significant figures based on the precision of the given measurements, assures that the density figure we report reflects our confidence in these measurements and complies with significant figure rules.