At 20 degrees celsius the vapor pressure of dry ice is 56.5
atm. If 10 g of dry ice (solid CO2) is placedin in an evacuated 0.25 L chamber at a constant temperature of 20 degrees celsius, will all of the solid sublime?
PV = nRT
Solve for n at the conditions listed, convert to grams CO2, and compare with 10 g you started with.
To determine whether all of the solid dry ice will sublime in the given conditions, we need to compare the vapor pressure of dry ice at 20 degrees Celsius to the pressure in the chamber.
First, we need to convert the mass of dry ice from grams to moles. The molar mass of CO2 is approximately 44 g/mol, so 10 g of dry ice is equivalent to 10 g / 44 g/mol = 0.227 moles of CO2.
Next, we can use the ideal gas law to calculate the pressure of the CO2 gas when all of the dry ice has sublimed. The ideal gas law equation is given by:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L × atm / K × mol)
T = temperature (in Kelvin)
The temperature is already given in degrees Celsius, so we need to convert it to Kelvin by adding 273.15:
T = 20 + 273.15 = 293.15 K
Considering an ideal gas, the volume of the chamber and the moles of CO2 will remain constant. Therefore, we can rearrange the ideal gas law equation to solve for the pressure:
P = nRT / V
Plugging in the values, we get:
P = (0.227 mol) * (0.0821 L × atm / K × mol) * (293.15 K) / 0.25 L
Calculating this gives us a pressure of approximately 21.4 atm.
Since the vapor pressure of dry ice at 20 degrees Celsius is 56.5 atm, and the pressure in the chamber is only 21.4 atm, it means that not all of the solid dry ice will sublime.