Problem 99 - Chemistry Principles and Practice

Question

The mass of a piece of metal is \(134.412 \mathrm{~g}\). It is placed in a graduated cylinder that contains \(12.35 \mathrm{~mL}\) water. The volume of the metal and water in the cylinder is found to be \(19.40 \mathrm{~mL}\). Calculate the density of the metal.

Step-by-Step Solution

Answer

The density of the metal is approximately 19.06 g/mL.

Step 1: Understand the Problem

We are given the mass of a metal and the initial and final volumes of water with the metal in a graduated cylinder. Our goal is to find the density of the metal.

Step 2: Identify Relevant Formulas

Density is calculated using the formula: \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). Here, the volume of the metal needs to be determined as the difference in water volume with and without metal.

Step 3: Calculate the Volume of Metal

The volume of the metal can be determined by subtracting the initial water volume from the total volume with metal. So, \( V_{\text{metal}} = 19.40 \text{ mL} - 12.35 \text{ mL} = 7.05 \text{ mL} \).

Step 4: Calculate the Density

Now that we have the mass of the metal (134.412 g) and its volume (7.05 mL), use the density formula: \( \text{Density} = \frac{134.412 \text{ g}}{7.05 \text{ mL}} \approx 19.06 \text{ g/mL} \).

Key Concepts

Mass Measurement

Understanding how to measure mass is fundamental in chemistry experiments. Mass refers to the amount of matter in an object, and it is typically measured in grams (g) using a digital or analytical balance.
In our exercise, the mass of the metal piece was accurately measured as \(134.412\, \text{g}\). Accurate mass measurement is crucial as small errors can lead to significant inaccuracies in density calculations.
When performing a mass measurement, make sure:

• The balance is correctly calibrated.
• The object is clean and not affected by moisture or residues.
• You take multiple readings to ensure accuracy.

Volume Displacement Method

The volume displacement method is an essential technique for determining the volume of an irregularly shaped object. This method involves submerging the object in a fluid, usually water, and measuring the amount of fluid displaced.
In our exercise, a graduated cylinder was used with initial water volume set at \(12.35\, \text{mL}\). When the metal was placed inside, the water level rose to \(19.40\, \text{mL}\). The difference in these volumes gave the exact volume of the metal, \(7.05\, \text{mL}\).

• Ensure the object is fully submerged for accurate results.
• Record the water level at eye level for precision.
• Subtract the initial volume from the new volume to calculate displacement.

Density Formula

Density is an important property that relates mass and volume. It tells us how tightly matter is packed in an object. The formula for density \( (\rho) \) is given by: \[ \rho = \frac{\text{Mass}}{\text{Volume}} \] In our case, knowing the mass \( (134.412\, \text{g}) \) and volume \( (7.05\, \text{mL}) \) allows us to calculate the density of the metal.
By substituting these values into the formula, we find that the density of the metal is approximately \(19.06\, \text{g/mL}\).

• Always use consistent units (e.g., grams and milliliters).
• Check your calculations for rounding accuracy.
• Consider the significance of your result related to material properties.

Problem Solving in Chemistry

Problem-solving in chemistry often involves breaking down the task into manageable steps, similar to our example. Here are some effective strategies:
Begin by clearly understanding the problem. Identify what information you are given and what you need to find.
Select the appropriate formulas or principles relevant to the problem, as we did when identifying the density formula.
Carefully execute calculations and check each step, ensuring all measurements are correct and properly used.

• Re-check your work to avoid simple errors.
• Relate your findings to theoretical concepts.
• Practice regularly to enhance your problem-solving skills.

By following such structured approaches, students can enhance their competency in tackling various challenges in chemistry.