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 81. °c and 1.0 atm. what will be the state of the sample? select suppose the temperature is held constant at 81. °c but the pressure is decreased by 0.5 atm. what will happen to the sample? select suppose, on the other hand, the pressure is held constant at 1.0 atm but the temperature is increased by 140. °c. what will happen to the sample? select

Explanation:

First Question:

Step1: Convert temperature to Kelvin

To use the phase diagram (which has temperature in Kelvin), convert \( 81^\circ\text{C} \) to Kelvin. The formula is \( T(\text{K}) = T(\text{°C}) + 273.15 \). So, \( 81 + 273.15 = 354.15 \, \text{K} \).

Step2: Analyze phase at 354.15 K and 1.0 atm

Looking at the phase diagram, at \( \approx 354 \, \text{K} \) (close to 354.15 K) and 1.0 atm, the region is labeled "liquid". So the state is liquid.

Second Question:

Step1: Find new pressure

Original pressure is 1.0 atm, decreased by 0.5 atm, so new pressure is \( 1.0 - 0.5 = 0.5 \, \text{atm} \). Temperature remains \( 354.15 \, \text{K} \).

Step2: Analyze phase change

At constant temperature (354.15 K), decreasing pressure from 1.0 atm to 0.5 atm. Looking at the phase diagram, moving left (decreasing pressure) at constant temperature from the liquid region, we cross into the gas region. So the sample will vaporize (change from liquid to gas).

Third Question:

Step1: Find new temperature

Original temperature is \( 81^\circ\text{C} \) (354.15 K), increased by \( 140^\circ\text{C} \), so new temperature is \( 81 + 140 = 221^\circ\text{C} \), converting to Kelvin: \( 221 + 273.15 = 494.15 \, \text{K} \). Pressure is constant at 1.0 atm.

Step2: Analyze phase change

At constant pressure (1.0 atm), increasing temperature from 354.15 K to 494.15 K. Looking at the phase diagram, moving right (increasing temperature) at constant pressure from the liquid region, we cross into the gas region. So the sample will boil (change from liquid to gas).

Answer:

s:

1. State of the sample at \( 81^\circ\text{C} \) and 1.0 atm: liquid
2. When pressure decreases by 0.5 atm at constant \( 81^\circ\text{C} \): vaporize (liquid to gas)
3. When temperature increases by \( 140^\circ\text{C} \) at constant 1.0 atm: boil (liquid to gas)