A piece of dry ice (solid carbon dioxide) with a mass of 5.40 g is placed in a 10.0 L vessel?
that already contains air at 715 torr and 25 degrees C. After the carbon dioxide has totally vaporized, what is the partial pressure of the carbon dioxide and the total pressure in the container at 25 degrees C?
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I assume the vessel is CLOSED.
Use PV = nRT and solve for pCO2.
n = grams CO2/molar mass CO2.
pair (from the problem) is 715 torr.
Ptotal = pCO2 + pair but not that pCO2 is in atm and pair is in torr.
To calculate the partial pressure of carbon dioxide and the total pressure in the container at 25 degrees Celsius, we need to use the ideal gas law equation. The ideal gas law equation is given by:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Ideal gas constant (0.0821 L.atm/mol.K)
T = Temperature
First, let’s calculate the number of moles of carbon dioxide using the molecular weight of carbon dioxide (44 g/mol) and the mass of dry ice (5.40 g):
Number of moles (n) = Mass / Molecular weight = 5.40 g / 44 g/mol ≈ 0.1227 mol
Next, let's calculate the partial pressure of carbon dioxide using the formula:
Partial Pressure of Carbon Dioxide = nRT / V
Plugging in the values:
Partial Pressure of Carbon Dioxide = (0.1227 mol) x (0.0821 L.atm/mol.K) x (298.15 K) / (10.0 L)
Partial Pressure of Carbon Dioxide ≈ 0.297 atm
Since the dry ice has completely vaporized, the partial pressure of carbon dioxide equals the total pressure in the container.
Therefore, the partial pressure of carbon dioxide and the total pressure in the container at 25 degrees Celsius is approximately 0.297 atm.
To determine the partial pressure of the carbon dioxide and the total pressure in the container after the dry ice has vaporized, you'll need to use the ideal gas law and Dalton's law of partial pressures.
1. Calculate the number of moles of carbon dioxide:
The molar mass of carbon dioxide (CO2) is 44.01 g/mol.
Number of moles = mass / molar mass
Number of moles = 5.40 g / 44.01 g/mol
2. Determine the new number of moles of gas in the container:
Since the carbon dioxide has completely vaporized, it will occupy the entire volume of the container. Thus, the number of moles of carbon dioxide will be the same as the total number of moles in the container.
3. Using the ideal gas law, calculate the total pressure in the container:
The ideal gas law equation is:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, convert the temperature from Celsius to Kelvin. Add 273.15 to the temperature.
T = 25°C + 273.15 = 298.15 K
Now, rearrange the ideal gas law equation to solve for pressure:
P = (nRT) / V
Substitute the values into the equation and calculate the pressure.
4. Determine the partial pressure of carbon dioxide:
According to Dalton's law of partial pressures, the total pressure in the container is the sum of the individual partial pressures of each gas present.
The partial pressure of carbon dioxide is equal to the total pressure since it is the only gas in the container after the dry ice has vaporized.
By following these steps, you can calculate both the partial pressure of carbon dioxide and the total pressure in the container at 25 degrees Celsius.