Problem 68 - Chemistry The Central Science In Si Units

Question

Ethyl chloride is sold as a liquid (see photo) under pressure for use as a local skin anesthetic. Ethyl chloride boils at \(12^{\circ} \mathrm{C}\) at atmospheric pressure. When the liquid is sprayed onto the skin, it boils off, cooling and numbing the skin as it vaporizes. (a) What changes of state are involved in this use of ethyl chloride? (b) What is the boiling point of ethyl chloride in degrees Fahrenheit? (c) The bottle shown contains \(103.5 \mathrm{~mL}\) of ethyl chloride. The density of ethyl chloride at \(25^{\circ} \mathrm{C}\) is \(0.765 \mathrm{~g} / \mathrm{cm}^{3} .\) What is the mass of ethyl chloride in the bottle?

Step-by-Step Solution

Answer

(a) Liquid to gas (vaporization); (b) 53.6°F; (c) 79.18 g.

Step 1: Identify the states of matter

When ethyl chloride is sprayed onto the skin, it goes from a liquid state at high pressure in the bottle to a gaseous state as it vaporizes on the skin. These changes of state involve a transition from liquid to gas, which is known as boiling or vaporization.

Step 2: Convert Celsius to Fahrenheit

To convert the boiling point of ethyl chloride from Celsius to Fahrenheit, use the formula: \[ F = \frac{9}{5}C + 32 \]Substituting the given boiling point:\[ F = \frac{9}{5} \times 12 + 32 \]\[ F = 21.6 + 32 \]\[ F = 53.6^{\circ} \mathrm{F} \]

Step 3: Calculate mass using density

To find the mass of ethyl chloride in the bottle, use the formula: \[ \text{Mass} = \text{Volume} \times \text{Density} \]Given volume is 103.5 mL and density is 0.765 g/cm³. Since 1 mL = 1 cm³, substitute these values into the formula:\[ \text{Mass} = 103.5 \times 0.765 \]\[ \text{Mass} = 79.1775 \text{ g} \]

Key Concepts

Understanding the States of Matter

In the world of chemistry, substances can exist in different forms called states of matter. The main states are solid, liquid, and gas. When we deal with a substance like ethyl chloride, its behavior in different states can have practical applications, such as its use as a skin anesthetic. In its liquid form, under pressure, ethyl chloride stays in the bottle. When you release it and spray it onto the skin, it transitions from a liquid to a gas. This change is called vaporization or boiling. The process of a liquid turning into a gas involves particles gaining energy and moving apart from each other, resulting in a state change. Here, the energy comes from the heat of the skin, which is absorbed by the liquid to cause the vaporization. This is why spraying ethyl chloride cools the skin - the liquid absorbs heat as it boils off, leaving the skin numbed.

Ethyl chloride is an excellent example of how the properties of a compound can be harnessed in real-world applications. It's essential for students to grasp the fundamental idea that matter can shift between states based on environmental conditions like temperature and pressure. This understanding is foundational in explaining not just physical changes but also how these changes are used in various scientific and medical fields.

Converting Boiling Points Between Celsius and Fahrenheit

Temperature is a key factor in the behavior of substances, especially when dealing with boiling points. For students tasked with boiling point conversion, it's often between the Celsius and Fahrenheit scales.

Ethyl chloride boils at \(12^{\circ}\mathrm{C}\). Converting this to Fahrenheit involves a straightforward formula:

• Start with the formula: \( F = \frac{9}{5}C + 32 \)
• Insert the given Celsius temperature: \( F = \frac{9}{5} \times 12 + 32 \)
• Solve the equation to find \( F = 53.6^{\circ} \mathrm{F} \)

This formula works because it mathematically aligns the two temperature scales, allowing easy conversion. Knowing how to convert between scales is particularly useful in chemistry and day-to-day life, as it enables you to interpret temperatures regardless of the scale used.

Understanding temperature conversions enhances comprehension of chemical reactions and physical changes, essential for experiments and practical applications. Students can further practice this skill by trying conversions with various substances and their respective boiling and freezing points.

Calculating Density and Mass

Density is an important property of matter that describes how much mass exists in a given volume. In designing experiments or practical applications with substances like ethyl chloride, knowing the density allows us to calculate mass from a known volume. This relationship is expressed with the formula:

• \( \text{Mass} = \text{Volume} \times \text{Density} \)

Given a volume of \(103.5 \text{ mL}\) and a density of \(0.765 \text{ g/cm}^3\), we can calculate the mass of ethyl chloride in a container:

• Convert volume into a suitable unit: Since \(1 \text{ mL} = 1 \text{ cm}^3\), use \(103.5 \text{ cm}^3\).
• Substitute into the formula: \( \text{Mass} = 103.5 \times 0.765 \)
• Calculate to find \( \text{Mass} = 79.1775 \text{ g} \)

This calculation is critical in fields where precision is necessary. Understanding density and its role in determining mass helps predict how substances will behave in real-world scenarios, such as manufacturing, food science, and medicine. It's a fundamental concept that bridges theoretical chemistry with practical applications.