Problem 102 - Beginning and Intermediate Algebra

Question

In forensics, the density of a substance is used to help identify it. The expression \(\frac{M}{V}\) represents the density of an object with a mass of \(M\) grams and a volume of \(V\) milliliters. Find the density of an object having a mass of 29.76 grams and a volume of 12 milliters.

Step-by-Step Solution

Answer

Density is 2.48 g/mL.

Step 1: Identify the Given Values

To find the density, we need the mass and volume of the object. The problem states that the mass \( M \) is 29.76 grams and the volume \( V \) is 12 milliliters.

Step 2: Write the Density Formula

The formula to calculate density \( D \) is given by the expression \( D = \frac{M}{V} \). Here, \( M \) represents the mass and \( V \) represents the volume.

Step 3: Substitute the Given Values into the Formula

Using the formula \( D = \frac{M}{V} \), substitute \( M = 29.76 \) grams and \( V = 12 \) milliliters into the equation. This yields \( D = \frac{29.76}{12} \).

Step 4: Calculate the Density

Now, perform the division \( \frac{29.76}{12} \) to find the density. The result is \( D = 2.48 \). Therefore, the density is 2.48 grams per milliliter.

Key Concepts

Understanding Mass

Mass is a fundamental property of matter, representing the amount of matter present in an object. It is a measure of how much "stuff" is inside something. In physics, mass is usually measured in grams or kilograms. Understanding mass is crucial when calculating density, as mass is one of the components in the density formula.Here are some points to remember about mass:

• Mass is constant for an object and does not change regardless of its location, contrasting with weight, which can vary depending on gravitational pull.
• Mass is measured using a balance or scale, and in science, it is often noted with the symbol \( M \).
• In this exercise, the mass given is 29.76 grams, a central value required for finding density.

Mass is a critical variable in many scientific calculations and ensures that measurements are precise, especially in areas like forensics, where identifying substances accurately is key.

Exploring Volume

Volume is the amount of space an object occupies. It is an important concept in density, as volume tells us how much space the mass is spread over. Volume can be measured in different units, but in the context of density calculations, it is commonly measured in milliliters or liters. Let's delve into more about volume:

• Volume for liquids and gases is often measured with graduated cylinders or burettes in scientific settings.
• For solids, volume can be determined by water displacement or mathematical formulas, depending on the shape of the object.
• In our exercise, the volume given is 12 milliliters. This piece of data helps us understand how compact the mass is.

Knowing how to measure and interpret volume is integral for sciences like chemistry and physics, and is especially used in forensics to help identify substances by their density.

The Role of Density in Forensics

Forensic scientists use density to identify unknown substances, as each material has a specific density. By measuring the density of a sample, forensic experts can compare it to known densities of substances to find a match. Here’s why density is so vital in forensic investigations:

• Density can help distinguish between substances that might look alike but have different compositional properties, such as different metals or minerals.
• Since density does not change with the amount of material present, it is a reliable property for identification tasks.
• For example, in our exercise, a calculated density of 2.48 grams per milliliter can help forensic scientists determine what the substance might be by comparing it with a database of known densities.

Understanding how to calculate and use density effectively can be a powerful tool in forensic science, aiding in the process of identifying and verifying substances in various scenarios.