Question

What is the density of a sample of \(65.0 \mathrm{~mL}\) of automobile oil having a mass of \(59.82 \mathrm{~g}\) ?

Short answer

The density is approximately 0.92 g/mL.

Step-by-step solution

Recall the Formula for Density

Density (\rho) is calculated by the formula: \[ \rho = \frac{m}{V} \] where \( m \) is mass and \( V \) is volume.

Identify Given Values

Given: \( m = 59.82 \ \text{g} \) and \( V = 65.0 \ \text{mL} \).

Substitute the Values

Substitute the given values into the density formula: \[ \rho = \frac{59.82 \text{g}}{65.0 \text{mL}} \]

Calculate the Density

Perform the division to find the density: \[ \rho = \frac{59.82}{65.0} \approx 0.920 \text{g/mL} \]

Key concepts

Density Formula

Density is a crucial concept in various fields such as physics, chemistry, and engineering. It helps us understand how much mass is present in a given volume of a substance. The formula for density is: \( \rho = \frac{m}{V} \).
Here, \( \rho \) represents density, \( m \) stands for mass, and \( V \) denotes volume.
By using this formula, we can determine how 'packed' the substance is within a specified space.
This basic yet powerful equation is useful for comparing different materials and understanding their properties.
For instance, a solid object with a higher density than water will sink, while a lower-density object will float.
To get the most accurate results, it's essential to measure both mass and volume correctly when calculating density.

Mass

Mass is a fundamental property of matter and a measure of the amount of substance in an object.
In the context of density, mass is represented by the symbol \( m \).
It is usually measured in units like grams (g) or kilograms (kg).
Accurate measurement of mass is crucial when calculating density.
For example, in the given exercise, the mass of the automobile oil is precisely \( 59.82 \) grams.
When measuring mass, it’s important to use a calibrated scale to ensure accuracy.
If you’re working with very small quantities, a more sensitive scale might be required.
Always remember to record the mass to the appropriate number of decimal places, based on the measurement tool's precision.

Volume

Volume is the amount of space that a substance or object occupies.
In the formula for density, volume is denoted by the symbol \( V \).
It is commonly measured in units such as milliliters (mL), liters (L), or cubic centimeters (cm³).
For example, in our exercise, the volume of the automobile oil is given as \( 65.0 \) mL.
Just like mass, accurate measurement of volume is crucial for calculating density.
Use appropriate tools like graduated cylinders or volumetric flasks to measure liquids.
Make sure to read the measurement at eye level and at the bottom of the meniscus for accuracy.
For solids, volume can sometimes be measured through water displacement methods.

Unit Conversion

Unit conversion is the process of converting one unit of measure to another.
It is an essential skill for working with measurements in science and engineering.
In the context of density, it's crucial that the mass and volume are in compatible units.
Common units for mass include grams (g) and kilograms (kg), and for volume, milliliters (mL) and liters (L).
For instance, converting grams to kilograms involves dividing by 1000, \( 1000 \text{g} = 1 \text{kg} \).
Similarly, converting milliliters to liters involves dividing by 1000, \( 1000 \text{mL} = 1 \text{L} \).
Always ensure that the units you are using in your calculations are consistent to avoid errors.
This consistency is especially important when using formulas like the density equation to ensure accuracy.