Give the physical state of CO2 under the following conditions: pressure = 4000 mmHg, temperature = 18 degrees F. show work!
To determine the physical state of CO2 under the given conditions, we need to use the phase diagram of carbon dioxide.
1. Start by converting the temperature from Fahrenheit to Celsius:
T(°C) = (T(°F) - 32) × 5/9
T(°C) = (18 - 32) × 5/9
T(°C) = -14.4°C
2. Convert the pressure from mmHg to atm:
1 atm = 760 mmHg
P(atm) = P(mmHg) / 760
P(atm) = 4000 mmHg / 760
P(atm) ≈ 5.26 atm
3. Refer to the phase diagram of CO2:
+-----------------+
| |
Gas | |
| |
+-----------------+
| |
| |
Liquid | |
| |
+-----------------+
| |
| |
Solid | |
| |
+-----------------+
The phase diagram shows the three states of matter for CO2: gas, liquid, and solid. The axes represent temperature (°C) and pressure (atm).
4. Locate the point on the phase diagram corresponding to the given conditions: -14.4°C and 5.26 atm.
From the diagram, we see that at temperatures below -56.6°C, CO2 is a solid. At temperatures above -56.6°C and pressures above approximately 5.1 atm, CO2 is a gas. Between these two temperature and pressure ranges, CO2 exists as a liquid.
Since -14.4°C and 5.26 atm fall within the range of temperatures above -56.6°C and pressures above 5.1 atm, the physical state of CO2 under these conditions is gas.
Therefore, CO2 in this scenario is in the gaseous state.