The vacancy fraction of a particular metal is found to double as the temperature of the metal is increased from 700 degrees C to 850 degrees C. Calculate the enthalpy of vacancy formation for this metal. Express your answer in units of eV.

STOP SPAMMING

Firstly, why is your caps lock on.

Secondly, asking a question is not spamming on a Q&A website. Asking many questions is fine. It just shows how you have no respect to other people, and that questions are only important if they are relevant to you.

If someone has a lot of legitimate questions, they have a lot of questions.
It is not spamming at all, it is asking for help.

This website is about answering questions. If someone has a lot of questions, you should try and answer them, not delete their questions.

What kind of idiotic logic is that? "Your contributions to this website were removed because there were too many."

Please, stop harassing people who are genuinely asking for help. It is what this website is for. Being inquisitive is fine.

0.435

To calculate the enthalpy of vacancy formation, we need to utilize the concept of equilibrium thermodynamics and the relation between the vacancy fraction and temperature. The vacancy fraction (f) is given by the following equation:

f = exp(-ΔHv / (k*T))

Where ΔHv is the enthalpy of vacancy formation, k is the Boltzmann constant (8.617333262145 x 10^-5 eV/K), and T is the temperature in Kelvin.

We are given that the vacancy fraction doubles as the temperature is increased from 700 degrees C to 850 degrees C. Therefore, we can set up the following equation:

2 * f1 = f2

Applying the equation for vacancy fraction to each temperature:

2 * exp(-ΔHv / (k * T1)) = exp(-ΔHv / (k * T2))

Since T1 = 700 °C = 700 + 273.15 = 973.15 K, and T2 = 850 °C = 850 + 273.15 = 1123.15 K, we can substitute these values into the equation:

2 * exp(-ΔHv / (8.617333262145 x 10^-5 * 973.15)) = exp(-ΔHv / (8.617333262145 x 10^-5 * 1123.15))

Taking the natural logarithm of both sides to simplify the equation:

ln(2) = -ΔHv / (8.617333262145 x 10^-5) * (1/973.15 - 1/1123.15)

Now, we can solve the equation for ΔHv by rearranging it:

ΔHv = -ln(2) * (8.617333262145 x 10^-5) * (1/973.15 - 1/1123.15)

Calculating this expression will give us the enthalpy of vacancy formation for the metal in eV.