Question

Calculate the density in grams per milliliter for each of the following. (a) $25.0\mathrm{mL}$ of ethyl alcohol having a mass of $19.7\mathrm{g}$ g (b) $10.0\mathrm{g}$ of ethyl ether having a volume of $14.0\mathrm{mL}$

Short answer

(a) 0.788 g/mL; (b) 0.714 g/mL.

Step-by-step solution

Understanding Density Formula

The density (\rho) of a material is calculated using the formula, $\rho =\frac{m}{V}$, where $m$ is the mass and $V$ is the volume. We will apply this formula to both parts (a) and (b) of the exercise.

Calculate Density for Ethyl Alcohol

For part (a), we have a volume $(V)$ of $25.0\text{mL}$ and mass $(m)$ of $19.7\text{g}$. Substitute to find density: $$\rho =\frac{19.7\text{g}}{25.0\text{mL}}=0.788\text{g/mL}$$.

Calculate Density for Ethyl Ether

For part (b), the mass $(m)$ is $10.0\text{g}$ and volume $(V)$ is $14.0\text{mL}$. Substitute these into the formula to find density: $$\rho =\frac{10.0\text{g}}{14.0\text{mL}}=0.714\text{g/mL}$$.

Key concepts

Understanding Mass

Mass is a fundamental concept in physics and chemistry, and it is crucial for calculating density. Sometimes, people mix up mass with weight, but it's important to remember they are different. Mass measures the amount of matter in an object, staying constant regardless of location, while weight is the force of gravity on an object, which can change depending on where you are in the universe.

Units of measurement for mass typically include:

• grams (g),
• kilograms (kg),
• milligrams (mg).

Understanding this concept helps you apply the mass properly in calculations to determine density accurately. In calculations, if a problem provides you with mass in kilograms or milligrams, converting it to grams might be required to keep your results consistent, especially when dealing with volumes in milliliters.

Comprehending Volume

Volume measures the space that an object occupies. It's a three-dimensional space, and this concept helps you understand how much space or capacity something has. In most density calculations like the ones in your exercises, the volume is measured in milliliters (mL) or cubic centimeters (cm³). Interestingly, 1 mL is precisely the same as 1 cm³, so you can use them interchangeably without affecting your calculations.

Some common units of volume include:

• milliliters (mL),
• liters (L),
• cubic meters (m³).

When working with density, it's crucial to pay attention to the units of both mass and volume. Ensuring the units align correctly means you'll get accurate density results every time.

Exploring the Density Formula

The density formula is your key to understanding how mass and volume interact. Written as $\rho =\frac{m}{V}$, it clearly shows that density $\rho$ is the mass $m$ of an object divided by its volume $V$. It is usually expressed in grams per milliliter (g/mL) or kilograms per cubic meter (kg/m³). However, when you're dealing with small objects or liquid samples, grams per milliliter is standard.

To make use of the density formula effectively:

• Ensure the mass and volume are in compatible units.
• Plug each value into the formula $\rho =\frac{m}{V}$.
• Solve to find the density.

Understanding this relationship helps in a variety of practical contexts, from determining whether an object will float on water to figuring out how much of material can fit in a container. It's a fundamental principle in science crucial for both theoretical and practical calculations.