- Calculate q, w, and ΔE for the vaporization of 12.5 g of liquid ethanol (C2 H5 OH) at 1.00 a

step 1 Okay, for the vaporization of C2H5OH, that is ethanol from liquid to C2H5 -ohethanol gas, we hav

- Calculate q, w, and ΔE for the vaporization of 12.5 g of...

- Calculate $q$, $w$, and $\Delta E$ for the vaporization of $12.5 \mathrm{~g}$ of liquid ethanol $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)$ at $1.00 \mathrm{~atm}$ at $78.0^{\circ} \mathrm{C}$, to form gaseous ethanol at $1.00$ atm at $78.0^{\circ} \mathrm{C}$. Make the following simplifying assumptions: (a) the density of liquid ethanol at $78.0^{\circ} \mathrm{C}$ is $0.789 \mathrm{~g} / \mathrm{mL}$, and (b) gaseous ethanol is adequately described by the ideal gas equation. The heat of vaporization of ethanol is $855 \mathrm{~J} / \mathrm{g}$.

- Calculate $q$, $w$, and $\Delta E$ for the vaporization of $12.5 \mathrm{~g}$ of liquid ethanol $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)$ at $1.00 \mathrm{~atm}$ at $78.0^{\circ} \mathrm{C}$, to form
gaseous ethanol at $1.00$ atm at $78.0^{\circ} \mathrm{C}$. Make the following simplifying assumptions: (a) the density of liquid ethanol at $78.0^{\circ} \mathrm{C}$ is $0.789 \mathrm{~g} / \mathrm{mL}$, and (b) gaseous ethanol is adequately described by the ideal gas equation. The heat of vaporization of ethanol is $855 \mathrm{~J} / \mathrm{g}$.

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Key Concepts

Enthalpy of Vaporization

This concept refers to the amount of energy required to convert a given mass of a liquid into its vapor phase at a constant temperature and pressure. It is expressed per unit mass (or mole) and when multiplied by the mass of a substance, it gives the heat required for vaporization.

Ideal Gas Law

The ideal gas law, represented as PV = nRT, relates the pressure, volume, temperature, and number of moles of a gas. It is used to calculate the change in volume when a substance undergoes a phase change from liquid to gas under constant temperature and pressure conditions.

Work in Thermodynamic Processes

Work in thermodynamics, particularly in processes involving gases, is often associated with volume changes against external pressure. In the context of vaporization, work is done by the system as the gas expands, and it can be calculated using the product of pressure and the change in volume.

First Law of Thermodynamics

The first law of thermodynamics states that energy is conserved in a system and can be expressed as ?E = q + w, where ?E is the change in internal energy, q is the heat added to the system, and w is the work done by the system. This principle is used to relate the heat absorbed during vaporization and the work done in expansion to determine the overall energy change.

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