Question

(a) A sample of carbon tetrachloride, a liquid once used in dry cleaning, has a mass of \(39.73 \mathrm{~g}\) and a volume of \(25.0\) mLat \(25^{\circ} \mathrm{C}\). What is its density at this temperature? Will carbon tetrachloride float on water? (Materials that are less dense than water will float.) (b) The density of platinum is \(21.45 \mathrm{~g} / \mathrm{cm}^{3}\) at \(20^{\circ} \mathrm{C}\). Calculate the mass of \(75.00 \mathrm{~cm}^{3}\) of platinum at this temperature. (c) The density of magnesium is \(1.738 \mathrm{~g} / \mathrm{cm}^{3}\) at \(20^{\circ} \mathrm{C}\). What is the volume of \(87.50 \mathrm{~g}\) of this metal at this temperature?

Short answer

(a) The density of carbon tetrachloride at 25°C is 1.589 g/mL. Since it is denser than water (density of water ≈ 1 g/mL), it will not float on water. (b) The mass of 75.00 cm³ of platinum at 20°C is 1608.75 g. (c) The volume of 87.50 g of magnesium at 20°C is approximately 50.35 cm³.

Step-by-step solution

Recall the density formula

Density is defined as mass per unit volume. The formula for density is: Density = \(\frac{mass}{volume}\)

Calculate the density of carbon tetrachloride

Given a mass of 39.73 g and a volume of 25.0 mL, we can find the density using the formula: Density = \(\frac{39.73\text{ g}}{25.0\text{ mL}}\) Density = 1.589 g/mL

Compare the density of carbon tetrachloride with water

The density of water at room temperature is approximately 1 g/mL. Since the density of carbon tetrachloride (1.589 g/mL) is greater than the density of water (1 g/mL), it is denser than water and will not float on it. #b# Calculate the mass of 75.00 cm³ of platinum at 20°C

Use the formula to find the mass of platinum

Given the density of platinum (21.45 g/cm³) and the volume (75.00 cm³), we can calculate the mass using the density formula: Mass = Density × Volume

Calculate the mass of platinum

Substitute the given values into the formula: Mass = \(21.45\frac{\text{g}}{\text{cm}^3}\) × \(75.00\text{ cm}^3\) Mass = 1608.75 g #c# Find the volume of 87.50 g of magnesium at 20°C

Rearrange the density formula to find the volume

From the density formula (Density = \(\frac{mass}{volume}\)), we can rearrange it to solve for volume: Volume = \(\frac{mass}{density}\)

Calculate the volume of magnesium

Given the mass of magnesium (87.50 g) and its density at 20°C (1.738 g/cm³), we can find the volume using the rearranged formula: Volume = \(\frac{87.50\text{ g}}{1.738\frac{\text{g}}{\text{cm}^3}}\) Volume ≈ 50.35 cm³

Key concepts

Mass and Volume Calculation

To understand how to calculate mass and volume, we must first be familiar with the concept of density. Density is a measure of how much mass is contained within a given volume. It's calculated using the formula:- **Density** = \( \frac{Mass}{Volume}\).When calculating the mass of a substance, if you know its density and volume, you can rearrange the density formula to find mass:- **Mass** = Density × Volume.
For example, in the case of platinum with a density of \(21.45 \text{ g/cm}^3\) and a volume of 75.00 cm³, you multiply these two values to find the mass:- \[Mass = 21.45 \text{ g/cm}^3 \times 75.00 \text{ cm}^3 = 1608.75 \text{ g}\].To find the volume of a substance when its mass and density are known, the formula can be rearranged as:- **Volume** = \( \frac{Mass}{Density}\).Taking magnesium as an example, with a mass of 87.50 g and a density of \(1.738 \text{ g/cm}^3\), you can calculate:- \[Volume = \frac{87.50 \text{ g}}{1.738 \text{ g/cm}^3} ≈ 50.35 \text{ cm}^3\].

This calculation method is vital in chemistry and physics as it allows scientists to understand how substances will behave under different conditions.

Properties of Matter

Matter is anything that has mass and takes up space. The properties of matter are essential for understanding how different substances interact with each other. There are two types of properties: physical and chemical.
- **Physical Properties**: These are aspects that can be observed or measured without changing the substance's identity. Examples include density, color, hardness, boiling and melting points. - **Chemical Properties**: These describe a substance's ability to undergo certain chemical changes. For example, iron rusting when exposed to oxygen. Density is a particularly important physical property because it helps characterize a substance. It's useful in separating materials and predicting their behavior in mixtures. In the context of the original exercise, knowing the density allows us to determine whether carbon tetrachloride will float or sink when placed in water.

Understanding these properties helps us predict how materials will react and combine in various scenarios, making it crucial for fields like material science and chemistry.

Density Comparison with Water

Comparing the density of a substance with water is a practical way to predict whether it will float or sink. Water has a standard density of approximately 1 g/mL at room temperature.

• If a substance has a lower density than water, it will float.
• If a substance has a higher density than water, it will sink.

In the case of carbon tetrachloride, its density is calculated to be 1.589 g/mL, while water’s density is about 1 g/mL. Since carbon tetrachloride's density is greater than water, it will sink when placed in water.
These comparisons are not only useful in academic problems but also have real-world applications. In the oil industry, for instance, the density comparison helps in designing containers and pipelines which ensure that less dense oil floats on water, facilitating easy recovery and separation.

Understanding these simple concepts forms the basis for more complex fluid dynamics studies that are critical in engineering and environmental science.