Assuming that 1 / 20 eV is required to liberate a molecule...

Assuming that $1 / 20 \mathrm{eV}$ is required to liberate a molecule from the surface of a certain liquid when $T=300 \mathrm{~K}$, what is the heat of vaporization in ergs/mole?
$$
\left[1 \mathrm{eV}=1.6 \times 10^{-12} \mathrm{erg}\right]
$$

Key Concepts

Mole Concept and Avogadro's Number

The mole is a fundamental unit in chemistry that represents a quantity of substance containing Avogadro's number (approximately 6.02 x 10^23) of entities, such as atoms or molecules. This concept allows for the conversion of energy per molecule to energy per mole, which is useful in macroscale thermodynamic calculations.

Electron Volt

An electron volt (eV) is an energy unit commonly used in physics and chemistry, defined as the amount of energy an electron gains when it is accelerated through an electric potential difference of one volt. It serves as a convenient unit for quantifying energies on the atomic or molecular scale.

Erg

An erg is a unit of energy in the centimeter-gram-second (CGS) system, widely used in various fields of physics. It is much smaller than the joule and is useful when expressing energies at small scales, such as molecular energies or energies involved in surface phenomena.

Heat of Vaporization

The heat of vaporization is the amount of energy required to convert one mole of a substance from the liquid phase to the gas phase at a constant temperature. It is an important thermodynamic quantity that reflects the strength of intermolecular forces within a liquid, influencing phenomena such as boiling and evaporation.

Transcript

0:00 Hi there.

00:01 So for this problem, we have water standing in the open at a temperature of 32 celsius degrees.

00:12 And it evaporates because of the escape of some of the surface molecules.

00:18 Now, the heat of vaporization is also given for water, and that is a value of 539 calories per.

00:32 Gram and is approximately equal to the product between epsilon and n, where epsilon is the tailf, the escape of some of, is the average energy of the escaping molecules and n is the number of molecules per gram.

01:04 So what we need to find for the first part of this problem is the average energy of the escaping molecules.

01:18 Now, to find this, we need first to find, well, we use this equation in here to obtain that, so that is the latin, the heat of vaporization over the number of molecules per gram.

01:43 Now, the molar mass of the atomic hydrogen, we know that that is one gram per mole.

01:52 And the molar mass of the atomic oxygen is 16 grams per mold.

01:59 Now, for water, we will have, since in water, we have two molecules of hydrogen and one molecule of oxygen.

02:09 So we will have, well, an atom, of course.

02:16 So that will be 1 plus 1 times 16.

02:20 So this will give us a value for water, the molar mass of the water, it's 18 grams per mole.

02:30 Now we know that they are the number of avogradges number, that's the number of molecules in a mole.

02:40 That is 6 .02 times 10 to 23.

02:44 Now what we can do is to divide this number by more to the minus 1 of course over the molar mass in order to obtain the number of molecules per gram.

03:08 So from here we obtain a value of 3 .34 times 10 to the 22 molecules per gram.

03:22 So what we can do is to substitute that value into the for the average energy of the escaping molecules...

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