Question

study the following phase diagram of substance x. use this diagram to answer the following questions. suppose a small sample of pure x is held at −93. °c and 15.8 atm. what will be the state of the sample? suppose the temperature is held constant at −93. °c but the pressure is decreased by 8.8 atm. what will happen to the sample? suppose, on the other hand, the pressure is held constant at 15.8 atm but the temperature is decreased by 77. °c. what will happen to the sample?

Explanation:

First Question:

Step1: Convert temperature to Kelvin

To convert Celsius to Kelvin, use the formula \( T(K) = T(^\circ C) + 273.15 \). For \( -93^\circ C \), we have \( T = -93 + 273.15 = 180.15 \, K \) (approx \( 180 \, K \)).

Step2: Analyze phase diagram

The pressure is \( 15.8 \, atm \) and temperature is \( 180 \, K \). Looking at the phase diagram, at this \( T \) and \( P \), the region is "liquid" (since between the solid - liquid and liquid - gas lines, and the temperature is above the triple - point temperature (around \( 100 \, K \)) and pressure is such that it's in the liquid region).

Step1: Find new pressure

Initial pressure \( P_1 = 15.8 \, atm \), pressure decrease \( \Delta P = 8.8 \, atm \), so new pressure \( P_2=15.8 - 8.8 = 7 \, atm \). Temperature is constant at \( T=-93^\circ C = 180 \, K \).

Step2: Analyze phase change

Looking at the phase diagram, at \( T = 180 \, K \), when pressure decreases from \( 15.8 \, atm \) to \( 7 \, atm \), we cross the liquid - gas boundary. So the liquid will vaporize (change to gas).

Step1: Find new temperature

Initial temperature \( T_1=-93^\circ C = 180 \, K \), temperature decrease \( \Delta T = 77^\circ C \), so new temperature \( T_2=-93 - 77=-170^\circ C \). Convert to Kelvin: \( T_2=-170 + 273.15 = 103.15 \, K \) (approx \( 103 \, K \)). Pressure is constant at \( 15.8 \, atm \).

Step2: Analyze phase change

Looking at the phase diagram, at \( P = 15.8 \, atm \), when temperature decreases from \( 180 \, K \) to \( 103 \, K \), we cross the liquid - solid boundary. So the liquid will freeze (change to solid).

Answer:

liquid

Second Question: