Step 1: Understanding the Question:
The question gives an equation connecting vapor pressures \(P_1\), \(P_2\) at temperatures \(T_1\), \(T_2\), through the enthalpy of vaporization \(\Delta H_v\), and asks which named law this is.
Step 2: Key Formula or Approach:
The Clausius-Clapeyron equation describes how the vapor pressure of a pure substance changes with temperature during a liquid to vapor phase change. Its differential form is
\[ \frac{dP}{dT} = \frac{\Delta H_v}{T \, \Delta V} \]
which, after using the ideal gas approximation for the vapor and integrating between two temperatures, gives the logarithmic (two-point) form.
Step 3: Detailed Explanation:
Integrating between \(T_1\) and \(T_2\), assuming \(\Delta H_v\) stays roughly constant over that range, gives
\[ \ln\left(\frac{P_2}{P_1}\right) = -\frac{\Delta H_v}{R}\left(\frac{1}{T_2}-\frac{1}{T_1}\right) \]
Rearranging and converting to base-10 log using the factor \(2.303\) gives exactly the form in the question,
\[ \log\left(\frac{P_1}{P_2}\right) = \frac{2.303 \, \Delta H_v (T_2 - T_1)}{R \, T_1 T_2} \]
This equation is used in physical pharmacy to find the heat of vaporization of a solvent or drug from vapor pressure readings taken at two known temperatures.
Step 4: Final Answer:
This equation is the Clausius-Clapeyron equation.