Question

A reaction requires \(21.5 \mathrm{~g}\) of \(\mathrm{CHCl}_{3}\). No balance is available, so it will have to be measured by volume. How many \(\mathrm{mL}\) of \(\mathrm{CHCl}_{3}\) need to be taken? (Density of \(\mathrm{CHCl}_{3}\) is \(1.484 \mathrm{~g} / \mathrm{mL}\).)

Short answer

Approximately 14.49 mL of \(\mathrm{CHCl}_{3}\) is needed.

Step-by-step solution

Identify the given quantities

The problem provides two pieces of information: the mass of \(\mathrm{CHCl}_{3}\) required (21.5 g) and its density (1.484 g/mL).

Write the formula for density

The formula for density is \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]. Rearranging this formula to solve for volume, we get \[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \].

Substitute the known values

Using the formula from the previous step, substituting the given mass \(21.5 \mathrm{g}\) and density \(1.484 \mathrm{g/mL}\), we have \[ \text{Volume} = \frac{21.5}{1.484} \approx 14.49 \mathrm{mL} \].

Calculate the volume

Perform the division: \[ 21.5 \div 1.484 = 14.49 \mathrm{mL} \].

Key concepts

Mass and Volume Relationship

In chemistry, understanding the relationship between mass and volume is essential for various calculations. Mass measures how much matter is in an object, usually in grams (g), and volume measures how much space an object occupies, typically in milliliters (mL) or liters (L).

When dealing with substances, knowing either the mass or volume can help determine the other if the density is known. This relationship is crucial for experiments where precise measurements are necessary, like when using chemical reagents.
For instance, if you only know the mass of a substance, using its density can help you find the volume you need. Conversely, if you have a volume measurement, you can use density to find the mass. This relationship simplifies many tasks in chemistry, making experimental procedures more straightforward.

Density Formula

Density is a fundamental concept in chemistry that relates mass to volume. The formula for density is:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
This formula shows that density is the mass of a substance divided by its volume. Density is typically expressed in units of grams per milliliter (g/mL) or grams per cubic centimeter (g/cm³).

To use the density formula for calculations, you can rearrange it to solve for either mass or volume, depending on what you need. For example, if you know the mass and density, you can find the volume by rearranging the formula to:
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]
Understanding how to manipulate and apply the density formula is key to performing accurate and meaningful chemistry experiments. This formula allows you to switch between mass and volume, making it versatile for various chemical calculations.

Unit Conversions in Chemistry

Unit conversions are vital in chemistry, as measurements must often be translated between different units to preserve accuracy and consistency. For density calculations, converting between units like grams (g), milliliters (mL), and cubic centimeters (cm³) is common.

Here are key things you need to remember about unit conversions in chemistry:

• 1 mL = 1 cm³: Milliliters and cubic centimeters are equivalent units of volume.
• 1 L = 1000 mL: Liters are larger units, often used in more extensive volume measurements.
• Use significant figures: Ensure the precision of your calculations by considering the number of significant figures given in the problem.

To illustrate this, let's look at our example problem where 21.5 g of \(\text{CHCl}_3\) needs to be converted to volume using its density (1.484 g/mL). By rearranging the density formula to solve for volume, you divide the mass by the density:
\[ \text{Volume} = \frac{21.5 \text{ g}}{1.484 \text{ g/mL}} \]
Incorporating unit conversions ensures measurements are accurate, aiding in reliable results for chemical reactions and solutions.