Problem 62 - Chemistry: The Central Science

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 a local skin anesthetic is from liquid to vapor (boiling). (b) The boiling point of ethyl chloride in degrees Fahrenheit is 53.6°F. (c) The mass of ethyl chloride in the bottle is approximately 79.173 grams.

Step 1: Identify the changes of state

First, let's identify the changes of state involved in the use of ethyl chloride as a local skin anesthetic. When ethyl chloride is sprayed onto the skin, it boils off (converts from liquid to vapor), cooling and numbing the skin as it vaporizes. Thus, the change of state involved here is from liquid to vapor (boiling).

Step 2: Convert boiling point to degrees Fahrenheit

To convert the boiling point of ethyl chloride from degrees Celsius to degrees Fahrenheit, we use the following formula: \(F = \frac{9}{5}(C) + 32\) Where F is the boiling point in degrees Fahrenheit, and C is the boiling point in degrees Celsius. Given boiling point in Celsius: \(C = 12^{\circ}\) Let's apply the formula: \( F = \frac{9}{5}(12) + 32 \) \( F = 53.6\) So, the boiling point of ethyl chloride in degrees Fahrenheit is 53.6°F.

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

To calculate the mass of ethyl chloride in the bottle, we will use the formula: \(mass = density \times volume\) Given density: \(0.765 \mathrm{g} / \mathrm{cm}^{3}\) Given volume: \(103.5 \mathrm{mL}\) Before proceeding, we need to convert the volume from mL to cm³, since 1 mL is equal to 1 cm³: \(103.5 \mathrm{mL} = 103.5 \mathrm{cm}^{3}\) Now, we can plug these values into our formula: \(mass = 0.765 \mathrm{g} / \mathrm{cm}^{3} \times 103.5 \mathrm{cm}^{3}\) \(mass = 79.173 \mathrm{g}\) So, the mass of ethyl chloride in the bottle is approximately 79.173 grams.

Key Concepts

Boiling Point

The boiling point of ethyl chloride is the temperature at which it changes from a liquid to a vapor. This characteristic is especially useful in its application as a local skin anesthetic. At atmospheric pressure, ethyl chloride boils at 12°C.

To better understand how temperature is perceived differently in varying contexts, converting this boiling point to Fahrenheit can be illuminating. Using the conversion formula, we have:

• Convert Celsius to Fahrenheit: \( F = \frac{9}{5}(C) + 32 \)
• Substitute 12 for \( C \): \( F = \frac{9}{5}(12) + 32 = 53.6°F \)

Understanding these conversions is helpful, especially if you are somewhere temperatures are generally reported in Fahrenheit. With a boiling point of 53.6°F, you can see how easily ethyl chloride vaporizes at room temperature conditions.

State Changes

State changes are fundamental to understanding how ethyl chloride works as an anesthetic. When sprayed on the skin, ethyl chloride undergoes a transition from liquid to vapor, known as boiling or vaporization.

This transition involves:

• Molecules gaining enough energy to break free from a liquid state
• Turning into gas upon reaching or exceeding the boiling point

As this happens, the ethyl chloride absorbs heat from the skin, creating a cooling effect. This heat absorption is what provides the numbing sensation beneficial in medical applications.

Observing these state changes helps reinforce how dynamic temperature and pressure relationships are in chemical substances.

Density

The density of a substance tells you how much mass it has in a particular volume. For ethyl chloride at 25°C, the density is given as 0.765 g/cm³. This means that each cubic centimeter of this liquid holds 0.765 grams of mass.

Understanding density is important for comparing substances and predicting behaviors under different conditions. Some key aspects include:

• The relationship between mass and volume
• How closely packed the molecules of a substance are
• Influence on floating or sinking behavior

In the case of ethyl chloride, its relatively low density compared to water might suggest some unique handling properties, especially when considering safety and storage conditions.

Mass Calculation

Calculating the mass from the density and volume is straightforward with ethyl chloride. Given:

• Density: 0.765 g/cm³
• Volume: 103.5 mL (which is the same as 103.5 cm³)

We can calculate the mass using the formula \( mass = density \times volume \).
Follow the steps:

• Substitute the known values: \( mass = 0.765 \times 103.5 \)
• Compute the mass: \( mass = 79.173 \, g \)

This provides an understanding of how much ethyl chloride is present in a given container, which is crucial for both application and safety management. Having a precise mass quantification ensures that you can assess how much product is necessary or remaining for use.