Problem 5 - Chemistry

Question

Chloroform, a substance once used as an anesthetic, has a density of \(1.483\) \(\mathrm{g} / \mathrm{mL}\) at \(20^{\circ} \mathrm{C}\). How many milliliters would you use if you needed \(9.37 \mathrm{~g}\) ? \(\left(1 \mathrm{~mL}=1 \mathrm{~cm}^{3}\right)\)

Step-by-Step Solution

Answer

The required volume is approximately 6.32 mL.

Step 1: Understand the Given Values

We are given the density of chloroform, which is \(1.483\, \mathrm{g/mL}\), and the mass that we need, which is \(9.37\, \mathrm{g}\). We need to find the volume in milliliters.

Step 2: Use the Density Formula

Recall that density \( (d) \) is defined as mass \( (m) \) divided by volume \( (V) \), i.e., \( d = \frac{m}{V} \). Rearrange this equation to find volume: \( V = \frac{m}{d} \).

Step 3: Substitute Given Values

Substitute the given mass \( (9.37\, \mathrm{g}) \) and density \( (1.483\, \mathrm{g/mL}) \) into the rearranged formula: \( V = \frac{9.37\, \mathrm{g}}{1.483\, \mathrm{g/mL}} \).

Step 4: Calculate the Volume

Perform the division: \( V = \frac{9.37}{1.483} \approx 6.32\, \mathrm{mL}\).

Step 5: Verify Units and Answer

Ensure the units make sense. Since we're dividing grams by grams per milliliter, the answer will be in milliliters. This matches our requirement.

Key Concepts

Mass and Volume Relationship

Understanding the mass and volume relationship is key to manipulating physical substances and solving related chemistry problems. This relationship revolves around the concept of density, which ties the two physical properties together in a straightforward way.
The mass of a substance is usually measured in grams, while its volume is often measured in milliliters or cubic centimeters. When dealing with density, it is essential to understand how mass and volume interact:

• The mass tells us how much matter is present in a given object.
• The volume indicates how much space that matter occupies.
• Together, they help us find out how closely packed the matter is, which is expressed through density.

These relationships are useful across various fields including chemistry, physics, and engineering, as they help us predict and calculate how much of a substance we need for certain processes.

Density Formula

The density formula is a powerful equation that links mass, volume, and density. It is expressed as:\[ d = \frac{m}{V} \]where \( d \) stands for density, \( m \) stands for mass, and \( V \) stands for volume. This formula helps calculate any one of the three variables, provided the other two are known.
To find the volume if density and mass are known, we rearrange the formula to:\[ V = \frac{m}{d} \]This rearrangement makes it simple to find how much space a set amount of substance will occupy. It can be applied not only to liquids like chloroform but also to solids and gases. Understanding and using the density formula is crucial to solving a range of scientific problems.

Unit Conversion in Chemistry

In chemistry, unit conversion is vital to ensure measurements are consistent with formulas and calculations. Different measurements often use different units, which is why conversion is necessary for accurate results.
For density calculations like the one for chloroform, it's important to ensure that:

• Mass is in grams and volume is in milliliters or cubic centimeters.
• Both units must align with the density unit, which is typically g/mL or g/cm³.
• Knowing that 1 mL equals 1 cm³ provides a handy conversion for volume measurements.

By mastering unit conversion, chemists can avoid potential errors in experiments and calculations. It facilitates communication of scientific information across the globe, regardless of the measurement systems in use across different regions.