at 20 C the vapor pressure of dry ice is 56.5 atm. if 32 g of dry ice is placed in an evacuated .25 l chamber at a constant temperature of 20 C will all the dry ice sublime
To determine if all the dry ice will sublime in the given conditions, we need to compare the vapor pressure of dry ice at that temperature to the pressure in the chamber.
To start, it is important to note that the vapor pressure of dry ice (solid carbon dioxide) depends on its temperature. At 20°C, the vapor pressure of dry ice is reported to be around 56.5 atm. This means that at this temperature, dry ice will begin to sublimate (transition from solid to gas) when the pressure reaches 56.5 atm.
Now, let's calculate the number of moles of dry ice in the chamber. We know that the molar mass of carbon dioxide (CO2) is approximately 44 g/mol.
Given:
Mass of dry ice = 32 g
Molar mass of CO2 = 44 g/mol
Number of moles = Mass / Molar mass
Number of moles = 32 g / 44 g/mol
Number of moles = 0.727 moles
Next, let's calculate the volume occupied by these moles of dry ice using the Ideal Gas Law equation:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Ideal Gas Constant (0.0821 L·atm/(mol·K))
T = Temperature in Kelvin
The temperature is given as 20°C, so we need to convert it to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 20°C + 273.15
T(K) = 293.15 K
Now we can rearrange the Ideal Gas Law equation to solve for volume:
V = nRT / P
Substituting the values, we get:
V = (0.727 moles) * (0.0821 L·atm/(mol·K)) * (293.15 K) / (P)
Given:
V = 0.25 L
P = ?
(n = 0.727 moles, R = 0.0821 L·atm/(mol·K), T = 293.15 K)
Solving for P:
P = (0.727 moles * 0.0821 L·atm/(mol·K) * 293.15 K) / 0.25 L
P ≈ 64.6 atm
Based on the calculation, the pressure in the chamber with 32 g of dry ice at a constant temperature of 20°C is approximately 64.6 atm, which is higher than the vapor pressure of dry ice at that temperature (56.5 atm).
Therefore, since the pressure in the chamber is higher than the vapor pressure of dry ice, all the dry ice will not sublime completely. Some of it will remain as solid.
To determine if all the dry ice will sublime, we can compare the vapor pressure of dry ice at 20°C with the pressure inside the chamber.
1. Convert the mass of dry ice to moles:
- The molar mass of carbon dioxide (CO2) is approximately 44 g/mol.
- The number of moles of dry ice is calculated as: moles = mass / molar mass
moles = 32 g / 44 g/mol ≈ 0.727 moles
2. Calculate the volume of 0.727 moles of CO2 at 20°C using the ideal gas law:
- The ideal gas law equation is: PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/(mol·K)), and T is temperature in Kelvin.
- Convert 20°C to Kelvin: T = 20°C + 273.15 ≈ 293.15 K
- Rearrange the ideal gas law equation to solve for V: V = nRT / P
V = (0.727 mol) * (0.0821 L·atm/(mol·K)) * (293.15 K) / 56.5 atm ≈ 1.584 L
3. Compare the volume of the dry ice to the volume of the chamber:
- The volume of the chamber is given as 0.25 L.
- Since the volume of the dry ice (1.584 L) is larger than the volume of the chamber (0.25 L), all the dry ice will not sublime completely. Some of it will remain as solid dry ice.
Therefore, all the dry ice will not sublime completely in the .25 L chamber at a constant temperature of 20°C.