Problem 104 - Chemistry Matter and Change

Question

Zinc Two separate masses of zinc were measured on a laboratory balance. The first zinc sample had a mass of 210.10 \(\mathrm{g},\) and the second zinc sample had a mass of 235.10 \(\mathrm{g} .\) The two samples were combined. The volume of the combined sample was found to be 62.3 \(\mathrm{mL}\) . Express the mass and density of the zinc sample in the correct number of significant figures.

Step-by-Step Solution

Answer

Mass: 445.20 g, Density: 7.15 g/mL (rounded to three significant figures).

Step 1: Calculate the Combined Mass

The first step is to calculate the total mass of the zinc samples by adding the masses of the two separate samples.\(210.10 \ \mathrm{g} + 235.10 \ \mathrm{g} = 445.20 \ \mathrm{g}\).

Step 2: Determine Significant Figures for Mass

Assess the number of significant figures for the combined mass. Both masses have five significant figures, so the total mass should be reported with five significant figures: \(445.20 \ \mathrm{g}\).

Step 3: Calculate the Density

Density is calculated using the formula \(\text{Density} = \frac{\text{Mass}}{\text{Volume}}\). Substituting the known values gives \(\frac{445.20 \ \mathrm{g}}{62.3 \ \mathrm{mL}} = 7.1461 \ \mathrm{g/mL}\).

Step 4: Determine Significant Figures for Density

The volume measurement, which has three significant figures, limits the precision of the calculated density. Therefore, the density should be rounded to three significant figures: \(7.15 \ \mathrm{g/mL}\).

Key Concepts

Mass Calculation

Mass calculation is a fundamental concept in chemistry that involves determining the total mass of a substance or a combination of substances. In the given exercise, two samples of zinc were measured separately and then their masses were combined.
One sample weighed 210.10 grams and the other 235.10 grams. When you combine these two masses, you simply add them together to get the total mass; thus, the calculation is:

• First zinc sample: 210.10 g
• Second zinc sample: 235.10 g
• Total mass: 210.10 g + 235.10 g = 445.20 g

When carrying out such mass calculations, it is essential to consider significant figures, which are the digits that carry meaning contributing to its measurement precision. In this case, since both measurements are recorded to four significant figures, the resulting sum should also maintain this precision, giving a total mass of 445.20 grams recorded to five significant figures. This practice helps ensure that the accuracy of your measurement results is maintained.

Density Calculation

Density is an important property of materials that defines how much mass is contained in a given volume. It is calculated using the formula:\[\text{Density} = \frac{\text{Mass}}{\text{Volume}}\]In our zinc exercise, we have already determined the combined mass to be 445.20 grams. The volume of the combined zinc sample is given as 62.3 milliliters. By substituting these values into the density formula, we calculate:\[\frac{445.20 \ \mathrm{g}}{62.3 \ \mathrm{mL}} = 7.1461 \ \mathrm{g/mL}\]
This calculation gives a raw result of 7.1461 g/mL. However, we need to apply the concept of significant figures to report the result accurately. Since the volume has three significant figures, it limits the overall precision of the density calculation. As a result, the density should be rounded to three significant figures, making it 7.15 g/mL.
Understanding density and its calculation is crucial in fields like chemistry and materials science because it provides insights into how substances will behave and interact.

Zinc Properties

Zinc is an essential metallic element found in many everyday products. It is characterized by several important properties that make it valuable for a wide range of applications.

• Density: As we calculated, zinc's density is approximately 7.15 g/mL. This property makes it relatively heavy and compact compared to many other metals.
• Corrosion Resistance: One of zinc's most notable properties is its resistance to corrosion, which is why it is often used for galvanizing steel or iron to protect against rust.
• Metallic Characteristics: Zinc has a bluish-silver appearance and is moderately conductive of electricity, which are common traits among metals.
• Role in Biology: In small amounts, zinc is essential for human health, playing a role in immune function, DNA synthesis, and enzyme activity.

By understanding zinc's properties, along with its mass and density, we can appreciate its versatility and importance both in industrial applications and biological systems. This knowledge is valuable not only for scientific study but for practical applications in engineering and health.