Question

Given $\Delta V_r$ and $\Delta S_r$ are the volume and entropy of reaction, respectively, the most suitable conditions for the reaction to be used as a geothermometer are

• A. small $\Delta V_r$ but large $\Delta S_r$
• B. small $\Delta S_r$ but large $\Delta V_r$
• C. positive $\Delta V_r$ but negative $\Delta S_r$
• D. negative $\Delta V_r$ but positive $\Delta S_r$

Hint:

Rule of thumb: Thermometers $\Rightarrow$ minimize $\Delta V$ (pressure effects) and maximize $\Delta S$ (temperature leverage). Barometers are the opposite—seek large $\Delta V$ and small $\Delta S$.

Answer 1

The Correct Option is A

Step 1: Pressure–temperature slope.
The Clapeyron relation for an equilibrium is \[ \frac{dP}{dT}=\frac{\Delta S_r}{\Delta V_r}. \] For a good geothermometer we want $T$ to be well constrained with minimal sensitivity to $P$.

Step 2: Conditions that reduce $P$-sensitivity and increase $T$-sensitivity.
- A small $\Delta V_r$ makes the equilibrium nearly insensitive to pressure (baric effect minimized).
- A large $\Delta S_r$ (hence often large $\Delta H_r$) makes the equilibrium strongly temperature dependent (steep $\frac{dP}{dT}$; isopleths are near-vertical, so uncertainty in $P$ produces little uncertainty in $T$).

Step 3: Eliminate alternatives.
(B) gives $P$-sensitive, $T$-insensitive behavior (good for barometers, not thermometers).
(C) and (D) give signs, not magnitudes; sign alone doesn't ensure thermometer suitability.

Final Answer:
\[ \boxed{\text{(A) small }\Delta V_r\ \text{but large }\Delta S_r} \]