Problem 48 - General Chemistry: Principles and Modern Applications

Question

A 15.2 L sample of chloroform at \(20^{\circ} \mathrm{C}\) has a mass of 22.54 kg. What is the density of chloroform at \(20^{\circ} \mathrm{C}\), in grams per milliliter?

Step-by-Step Solution

Answer

The density of the chloroform at \(20^{\circ} \mathrm{C}\) is approximately \(1.48 \) g/ml.

Step 1 Convert units

The mass is given in kilograms and it has to be converted into grams since the result is to be obtained in grams per milliliter. Similarly, the volume is provided in liters, and we should convert it to milliliters. To convert kilograms to grams, multiply the number of kilograms by 1000 as 1 kg contains 1000 grams. To convert liters into milliliters, again multiply by 1000 because 1L constitutes 1000ml. So, the mass becomes \(22540 \) grams and the volume becomes \(15200 \) milliliters.

Step 2 Calculate the density

Now with weight and volume in appropriate units, use the formula for calculating density, which is \( Density = Mass / Volume \). Plug the numbers to get the density, i.e., \( Density = 22540g / 15200ml \).

Step 3 Simplify the calculation

Divide \( 22540 \) by \( 15200 \) to find the density. Once the division is done, you will get the estimated density of the chloroform.

Key Concepts

Unit Conversion

Understanding unit conversion is essential in solving problems involving measurements in different units. Here, both mass and volume need to be converted for easy calculation of density.

For mass, if it’s initially in kilograms, like 22.54 kg in this case, you multiply by 1000 to convert to grams. This is because 1 kilogram is equivalent to 1000 grams.

• 22.54 kg x 1000 = 22540 grams

Similarly, the volume must be converted from liters to milliliters. Since 1 liter equals 1000 milliliters, multiply the given volume by 1000.

• 15.2 L x 1000 = 15200 milliliters

Mastering these simple multiplication conversions helps in standardizing units to make calculations consistent and accurate.

Density Formula

The density formula is a simple yet vital equation in dealing with mass and volume in various scientific contexts. It determines how much mass is present in a given volume. The formula is expressed as:

\[ \text{Density} (\rho) = \frac{\text{Mass} (m)}{\text{Volume} (V)} \]
Here, \( \rho \) denotes density, \( m \) is mass, and \( V \) represents volume. The units of the result depend on the input units. Achieving density in grams per milliliter requires converting inputs into grams for mass and milliliters for volume.

Once you have mass and volume in consistent units, simply divide the mass by the volume to get the density.

• Example calculation: \( 22540 \, \text{g} / 15200 \, \text{ml} \)

Knowing and using this formula is fundamental for calculating equilibrated physical properties in varied scientific expressions.

Chloroform Density

Chloroform is a chemical compound with specific physical properties, and understanding its density at certain conditions helps in practical applications in science and industry. At \( 20^{\circ} \text{C} \), you'll need to calculate the density using converted mass and volume from the sample.

With our problem parameters, the density of chloroform was calculated using the previously discussed formula:

• Mass = 22540 grams
• Volume = 15200 milliliters

Plug these values into the density equation:
\[ \text{Density} = \frac{22540\, \text{g}}{15200\, \text{ml}} \approx 1.482 \text{ g/ml} \]
Understanding chloroform's density, especially at room temperature, is vital for its safe handling and application in processes like HVAC, medical practices, and chemical manufacturing. It also plays a role in predicting how it's stored or mixed with other substances.