Problem 68 - Chemistry: The Central Science in SI Units, Global Edition

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) The change of state involved in the use of ethyl chloride as an anesthetic is from liquid to vapor. (b) The boiling point of ethyl chloride in degrees Fahrenheit is \(F = \frac{9}{5} \times 12 + 32 = 53.6^{\circ} \mathrm{F}\). (c) The mass of ethyl chloride in the bottle is calculated as Mass = 103.5 cm³ × 0.765 g/cm³ ≈ 79.2 g.

Step 1: Identify the changes of state

Ethyl chloride boils at 12°C at atmospheric pressure and is used as a local skin anesthetic. When it is sprayed onto the skin, it vaporizes. So, the change of state involved in this process is: Liquid ethyl chloride → Vapor ethyl chloride

Step 2: Convert boiling point from Celsius to Fahrenheit

To convert the boiling point of ethyl chloride from Celsius to Fahrenheit, we can use the following formula: \(F = \frac{9}{5} C + 32\) where F is the temperature in Fahrenheit, and C is the temperature in Celsius. Given the boiling point of ethyl chloride in Celsius is 12°C, we can find the boiling point in Fahrenheit as follows: \(F = \frac{9}{5} \times 12 + 32\) Calculate the value of F to find the boiling point in Fahrenheit.

Step 3: Calculate the mass of ethyl chloride in the bottle

We are given the volume of ethyl chloride in the bottle (103.5 mL) and its density at 25°C (0.765 g/cm³). We can use the following formula to find the mass of ethyl chloride in the bottle: Mass = Volume × Density First, let's convert the volume from mL to cm³ as 1 mL = 1 cm³. So, the volume of ethyl chloride is 103.5 cm³. Now, let's find the mass of ethyl chloride in the bottle: Mass = 103.5 cm³ × 0.765 g/cm³ Calculate the mass of ethyl chloride in the bottle.

Key Concepts

Boiling Point Conversion

When dealing with temperature conversions, it's helpful to understand how different temperature scales work. The boiling point of ethyl chloride is given as 12°C, and we can convert this value into Fahrenheit using a straightforward formula. The relationship between Celsius and Fahrenheit is given by the equation:\[ F = \frac{9}{5}C + 32 \]Here, \(C\) represents degrees Celsius and \(F\) degrees Fahrenheit.
To perform the conversion for ethyl chloride:

• Substitute 12°C into the equation.
• Calculate: \(F = \frac{9}{5} \times 12 + 32\).
• First, multiply \(\frac{9}{5}\) by 12 to get 21.6.
• Add 32 to 21.6 to get 53.6.

Thus, the boiling point of ethyl chloride in Fahrenheit is 53.6°F. Understanding this conversion is crucial, especially if you often switch between temperature scales.

Density Calculation

Density is a property that shows how much mass is contained within a certain volume. For ethyl chloride, we're given:

• Volume: 103.5 mL (which is equivalent to 103.5 cm³ since 1 mL equals 1 cm³).
• Density: 0.765 g/cm³ at 25°C.

By using the formula for mass, which is\[ \text{Mass} = \text{Volume} \times \text{Density} \],we can find the mass of ethyl chloride in the bottle.
Here's the step-by-step calculation:

• Multiply the volume (103.5 cm³) by the density (0.765 g/cm³).
• The resulting calculation is: Mass = 103.5 cm³ \( \times \) 0.765 g/cm³ = 79.1775 g.

Thus, the mass of the ethyl chloride in the bottle is approximately 79.18 grams. This calculation is simple but fundamental for figuring out how much material is present based on its volume and density.

Phase Change

Phase change refers to the transformation of a substance from one state of matter to another. Ethyl chloride undergoes a phase change when it is used as a local skin anesthetic:

• Initial State: Liquid ethyl chloride
• Final State: Vapor ethyl chloride

This process occurs at its boiling point, where the liquid absorbs energy to become gas. Upon spraying ethyl chloride on the skin, it gains enough energy from the surrounding environment, resulting in evaporation or vaporization.
This phase change is critical in the numbing effect:

• As the liquid vaporizes, it absorbs heat energy from the skin.
• This absorption of heat results in a cooling effect, thus numbing the area.
• The rapid transition from liquid to vapor helps in quick relief.

Understanding this phase change is essential in knowing how certain substances are used for medicinal or practical purposes.