Problem 45 - Chemistry: Principles and Reactions

Question

The cup is a measure of volume widely used in cookbooks. One cup is equivalent to \(225 \mathrm{~mL}\). What is the density of clover honey (in grams per milliliter) if three quarters of a cup has a mass of 252 g?

Step-by-Step Solution

Answer

Answer: The density of clover honey is approximately 1.493 g/mL.

Step 1: Find the volume of three-quarters of a cup

Since 1 cup is equivalent to 225 mL, we can find the volume of three-quarters of a cup by multiplying the volume of 1 cup by 0.75, which is: Volume of three-quarters of a cup = 0.75 * Volume of 1 cup Volume of three-quarters of a cup = 0.75 * 225 mL

Step 2: Calculate the volume

Now, we'll calculate the volume of three-quarters of a cup of honey: Volume = 0.75 * 225 mL = 168.75 mL

Step 3: Use the density formula

We'll now use the formula for density: Density = Mass / Volume We're given that the mass of the honey is 252 g, and we've calculated the volume to be 168.75 mL. Therefore, the density of clover honey is: Density = 252 g / 168.75 mL

Step 4: Calculate the density

Finally, let's find the density of clover honey: Density = 252 g / 168.75 mL ≈ 1.493 g/mL So, the density of clover honey is approximately 1.493 grams per milliliter.

Key Concepts

Volume Conversion

When handling different units of volume, especially in practical applications like cooking, it's essential to understand how to convert them accurately. In our given exercise, the volume is initially provided in cups, which we need to convert to milliliters (mL) to solve the problem correctly.

• A full cup is defined as 225 mL, which is a standard measurement.
• To find the volume of three-quarters of a cup, multiply the full cup volume by 0.75.
• This conversion results in a volume of 168.75 mL for three-quarters of a cup.

Understanding volume conversion is crucial not just in academic exercises but also in real-world scenarios, where various measurement systems are in use. This step ensures you have a consistent unit to perform calculations accurately.

Density Formula

Density is a fundamental concept in physics and chemistry, providing insight into how much mass is present in a given volume. The formula for density is straightforward:

• Density (\(D\)) is calculated by dividing mass (\(m\)) by volume (\(V\)).
• The formula is expressed as: \(D = \frac{m}{V}\).

In our problem, we are asked to find the density of clover honey, given its mass is 252 grams and the volume is 168.75 mL.
By applying the density formula, we substitute the given values into \(D = \frac{252 \, ext{g}}{168.75 \, ext{mL}}\).
This calculation will provide the density in grams per milliliter (g/mL), highlighting how tightly the mass is packed within the clover honey's volume.

Mass-Volume Relationship

Understanding the mass-volume relationship is vital to solving density-related problems, and it helps paint a broader picture of the material's properties. Essentially, this concept describes how mass correlates with the space it occupies.

• Mass refers to how much matter is present.
• Volume indicates how much space that matter takes up.

In this exercise, knowing that three-quarters of a cup of clover honey weighs 252 grams allows us to explore this relationship. By dividing the mass by the volume, we can ascertain how dense the substance is. The outcome tells us that, at approximately 1.493 g/mL, clover honey is relatively dense compared to other substances, meaning it has a substantial amount of mass in a small volume.