Question

A \(25.0-\mathrm{mL}\) sample of water at \(90^{\circ} \mathrm{C}\) has a mass of \(24.12 \mathrm{~g}\). Calculate the density of water at this temperature.

Short answer

The density of water at 90°C is approximately 0.9648 g/mL.

Step-by-step solution

- Understand the formula for density

Density is defined as the amount of mass per unit volume. The formula to calculate density is: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]

- Identify given values

From the exercise, we are given: - Mass (m) = 24.12 g - Volume (V) = 25.0 mL

- Calculate the density

Using the formula: \[ \text{Density} = \frac{24.12 \text{ g}}{25.0 \text{ mL}} \] Simplifying this: \[ \text{Density} = 0.9648 \text{ g/mL} \]

- Report the density

The density of water at \(90^{\text{ \text{C}}} \) is approximately 0.9648 g/mL.

Key concepts

Mass and Volume Relationship

To fully understand density, we need to grasp the relationship between mass and volume. Mass tells us how much matter an object contains. It's measured in grams (g) in our example.
Volume, on the other hand, tells us the space that the object occupies, measured in milliliters (mL) here.
The connection between mass and volume is integral to calculating density:

• When you divide mass by volume, you get the density.
• This tells you how much mass is packed into a given volume.
• Density can change if the object's mass or volume changes, even if slightly.

Understanding this connection helps us know how different materials compare. For example, something with high density has more mass in a given space than something with low density.

Water Density

Water density is a critical property to understand because it varies with temperature.

• At room temperature (around 25°C), water has a density of about 1 g/mL.
• As the water heats up, its molecules move faster and tend to occupy more space.

That’s why, at higher temperatures like 90°C, the density drops to approximately 0.9648 g/mL, as seen in our exercise.
This example shows how significant temperature changes impact physical properties like density, making accurate measurements and conditions essential.

Physical Properties

Physical properties are characteristics of a substance that can be observed or measured without changing the substance's chemical identity.
Density is a prime example of such a property. Other physical properties include:

• Color
• Boiling Point
• Melting Point
• Hardness

Understanding physical properties like density helps us predict how substances will behave in different situations and under various conditions. This knowledge is fundamental in fields ranging from cooking to industrial manufacturing.