Question

The familiar "ether" used as an anesthetic agent is diethyl ether, \(\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}\). Its heat of vaporization is \(+26.5 \mathrm{~kJ} / \mathrm{mol}\) at its boiling point. How much energy in kilojoules is required to convert 100 mL of diethyl ether at its boiling point from liquid to vapor if its density is \(0.7138 \mathrm{~g} / \mathrm{mL}\) ?

Short answer

Approximately 25.53 kJ of energy is required.

Step-by-step solution

Calculate Moles of Diethyl Ether

First, we need to calculate the mass of diethyl ether in 100 mL. Given the density is \(0.7138 \text{ g/mL}\), the mass is \(100 \text{ mL} \times 0.7138 \text{ g/mL} = 71.38 \text{ g}\). Next, we determine the molar mass of diethyl ether (\(\text{C}_4\text{H}_{10}\text{O}\)): \(4\times12.01 + 10\times1.008 + 16.00 = 74.12 \text{ g/mol}\). Therefore, the number of moles \(n\) is \(\frac{71.38 \text{ g}}{74.12 \text{ g/mol}} \approx 0.963 \text{ moles}\).

Calculate Energy Required for Vaporization

Using the heat of vaporization \(\Delta H_{vap} = 26.5 \text{ kJ/mol}\), the total energy \(Q\) required can be calculated using the formula \(Q = n\times \Delta H_{vap}\). Substituting the values, \(Q = 0.963 \text{ moles} \times 26.5 \text{ kJ/mol} \approx 25.53 \text{ kJ}\).

Key concepts

Diethyl Ether

Diethyl ether, with the chemical formula \( \mathrm{C}_{4}\mathrm{H}_{10}\mathrm{O} \), is a well-known solvent that was historically used as an anesthetic agent. This compound is part of the ether family, a group of organic chemicals where two alkyl groups are bonded to an oxygen atom. Diethyl ether is particularly known for its low boiling point, high volatility, and distinctive smell.

In the realm of chemistry and industry, diethyl ether is utilized extensively due to its solvent properties. It's used in laboratories for reactions that require a medium that can quickly evaporate. As a point of caution, due to its high flammability, diethyl ether must be handled with care, stored properly, and used in well-ventilated areas.

Understanding the properties and safe handling of diethyl ether is crucial, especially when performing experiments or industrial processes that involve its conversion between liquid and vapor forms.

Energy Calculation

Energy calculation is a fundamental concept in chemistry, particularly when dealing with phase changes such as from liquid to vapor. The energy required for a phase change is often quantified by the heat of vaporization. This value represents the amount of energy needed to convert one mole of a liquid into vapor at its boiling point.

To calculate the energy required for the vaporization of a specific amount of a chemical, you must first determine the number of moles of the substance present. This is done using the molecular weight and the mass of the sample involved. Once you know the number of moles, apply the heat of vaporization to calculate the total energy required. The formula used is:

\[ Q = n \times \Delta H_{vap} \]

where \( Q \) is the energy in kilojoules, \( n \) is the number of moles, and \( \Delta H_{vap} \) is the heat of vaporization.

Chemical Density

Density is a key property of substances in chemistry. It is defined as the mass per unit volume and is commonly expressed in grams per milliliter (g/mL) for liquids. Understanding the density of a substance allows chemists to relate its volume to its mass, which is essential for stoichiometric calculations in reactions.

In the context of our exercise, the density of diethyl ether is given as \( 0.7138 \mathrm{~g/mL} \). This means that each milliliter of diethyl ether weighs 0.7138 grams. This density allows us to calculate the mass of a specific volume with ease:

- For 100 mL of diethyl ether, the mass is calculated by multiplying the volume by the density:
\[ \text{Mass} = 100 \, \text{mL} \times 0.7138 \, \text{g/mL} = 71.38 \, \text{g} \]

Knowing mass is the first step in determining the moles needed for energy calculations.

Boiling Point

The boiling point of a substance is the temperature at which its liquid form turns into vapor. It is a crucial factor when studying phase changes and is determined by the ambient pressure. For diethyl ether, this temperature is relatively low compared to water, allowing it to convert to vapor easily at typical laboratory conditions.

The heat of vaporization is measured at the boiling point, signifying how much energy is needed to break the intermolecular forces holding the liquid together to convert it into a gaseous state. This concept is particularly important when calculating the energy required in processes involving vaporization at this temperature.

Understanding boiling point is essential for safely managing and using volatile substances like diethyl ether, preventing unwanted evaporation or physical hazards.