Problem 73 - Chemistry The Molecular Nature of Matter

Question

Calculate the density of kerosene, in \(\mathrm{g} / \mathrm{mL},\) if its mass is \(36.4 \mathrm{~g}\) and its volume is \(45.6 \mathrm{~mL}\).

Step-by-Step Solution

Answer

The density of kerosene is \(0.798 \mathrm{g/mL}\).

Step 1: Understand the Concept of Density

Density is a measure of how much mass is contained in a given volume. It can be calculated using the formula: density = \( \frac{mass}{volume} \).

Step 2: Gather the Given Data

From the exercise, we have the mass of the kerosene as \(36.4 \mathrm{g}\) and the volume of the kerosene as \(45.6 \mathrm{mL}\).

Step 3: Plug Values into the Density Formula

Using the formula for density, replace the mass and volume with the given values: \( \text{density} = \frac{36.4 \mathrm{g}}{45.6 \mathrm{mL}} \).

Step 4: Calculate the Density

Divide the mass by the volume to find the density: \( \text{density} = \frac{36.4}{45.6} = 0.7982 \mathrm{g/mL} \) (rounded to four decimal places).

Step 5: State the Final Answer

Round the value of density to an appropriate number of significant figures based on the given data. In this case, the mass and volume measurements are given to three significant figures, so the density should be reported to three significant figures: \( 0.798 \mathrm{g/mL} \).

Key Concepts

Density Formula

Understanding how to calculate the density of a material is an essential skill in various scientific disciplines. Calcualting density allows us to compare the compactness of different substances. The density formula is the relationship between the mass of a substance and its volume, which is generally expressed as:
\[\begin{equation}density = \frac{mass}{volume}\end{equation}\]
By using this formula, you can determine the density of any material as long as you have its mass and volume. For example, given a mass of \(36.4\,g\) and a volume of \(45.6\,mL\), the density of kerosene can be calculated by simply dividing the mass by the volume. This calculation is fundamental to many laboratory and real-world applications, ranging from identifying the purity of a sample to designing objects that must float or sink in fluids.

Significant Figures

Significant figures, also known as significant digits, are crucial in the world of measurements and calculations. They indicate the precision of a measurement by showing which digits are meaningful and derived from actual measurements or estimations.
In the example of calculating the density of kerosene, both the mass and volume are provided to three significant figures. When performing calculations, it is vital to ensure that your final answer reflects the precision of the measurements used. If we calculated the density to be \(0.7982\,g/mL\), we must round this to three significant figures, resulting in \(0.798\,g/mL\). By respecting significant figures, we communicate the reliability of our results and maintain scientific accuracy. Whenever you are reporting your final values, always check your significant digits to appropriately reflect the certainty of your measurements.

Mass to Volume Ratio

In the context of density, the mass to volume ratio conveys how much mass is located within a unit volume of a substance. Expressed mathematically, it's simply the mass of an object divided by its volume. This concept is the crux of density and is directly used in its calculation.
A low mass to volume ratio will result in a low density, indicating that the substance is comparatively lighter or less compact. Conversely, a high ratio implies a denser, more compact material. In our kerosene example, where the mass is \(36.4\,g\) and the volume is \(45.6\,mL\), the mass to volume ratio helps us understand how tightly packed the kerosene molecules are within that space. Through this understanding, different substances can be compared, objects can be designed to sink or float, and material properties can be inferred, demonstrating the broad utility of this simple yet powerful concept.