Problem 66 - Chemistry Matter and Change

Question

A 5-mL sample of water has a mass of 5 \(\mathrm{g} .\) What is the density of water?

Step-by-Step Solution

Answer

The density of water is 1 g/mL.

Step 1: Understand the Formula for Density

Density is defined as mass divided by volume. The formula for density \( \rho \) is: \( \rho = \frac{\text{mass}}{\text{volume}} \). In this problem, we will use this formula to determine the density of the water sample.

Step 2: Identify the Given Values

From the problem, we have a mass of 5 grams and a volume of 5 milliliters. These will be used as the inputs for the density formula.

Step 3: Substitute the Values into the Formula

Using the formula from Step 1, substitute the given mass and volume into the formula: \( \rho = \frac{5 \, \text{g}}{5 \, \text{mL}} \).

Step 4: Calculate the Density

Perform the division in the formula: \( \rho = \frac{5}{5} = 1 \, \text{g/mL} \). This calculation shows that the density of the water is 1 gram per milliliter.

Key Concepts

Mass and Volume

Mass and volume are two fundamental properties that help us understand the physical characteristics of a substance. Mass refers to the amount of matter contained in an object and is usually measured in grams or kilograms. It's important to remember that the mass of an object remains constant regardless of its location in the universe.

Volume, on the other hand, is the amount of space that an object occupies. It is commonly measured in units such as milliliters or liters for liquids and cubic centimeters or meters for solids. To visualize volume, think of how much liquid can fill a container, like a cup or a bottle.

Understanding the relationship between mass and volume is crucial when it comes to calculating the density of a substance. It's the interplay between these two elements that allows us to determine how concentrated or "packed" a substance is.

Water Density

Water density is a key concept in both science and everyday life. It describes how compact the molecules in water are arranged, which is a crucial factor in many physical and chemical phenomena. The density of water is generally accepted to be 1 gram per milliliter (g/mL) at its maximum density, which occurs at 4 degrees Celsius.

Water's density plays a vital role in nature and the environment. For instance, it influences ocean currents, the buoyancy of objects in water, and even weather patterns. This density is also why ice floats on water; as water freezes, it expands rather than contracts, making ice less dense than liquid water.

Moreover, understanding water density is significant for scientific experiments and industrial applications, where precise measurements are essential.

Density Formula

The density formula is a simple yet powerful mathematical tool. It is used to assess how much mass is present in a given volume. The formula is expressed as:

• Density () = Mass / Volume

This equation helps determine how concentrated a substance is.

In practical terms, using this formula requires two essential steps: identifying the measured mass and volume of the substance. Once you have these values, you substitute them into the formula. For example, with a mass of 5 grams and a volume of 5 milliliters:

• The calculation is  = \( \frac{5\,\text{g}}{5\,\text{mL}} \)

Performing this division gives you a density of 1 g/mL, which is the commonly recognized density of water at room temperature.

This formula is not exclusive to water; it can be applied to any substance, offering a universal method to calculate density across various materials.