A 1.10 sample of dry ice is added to a 745 mL flask containing nitrogen gas at a temperature of 25.0 degrees C and a pressure of 735 mm Hg . The dry ice is allowed to sublime (convert from solid to gas) and the mixture is allowed to return to 25.0 degrees C.
What is the total pressure of the flask?
Any help would be greatly appreciated.
How many moles N2 do you have initially? That will be n = PV/RT.
Then you will add how many moles CO2? That will be moles = grams/molar mass.
Then rework PV = nRT with total moles and solve for total P.
To solve this problem, we can use the ideal gas law:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
We can assume that the nitrogen gas behaves ideally.
Step 1: Convert the temperature to Kelvin
To convert from degrees Celsius to Kelvin, we add 273.15.
T₁ = 25.0 + 273.15 = 298.15 K
Step 2: Calculate the initial number of moles of nitrogen gas
We can use the ideal gas law to calculate the initial number of moles of nitrogen gas.
P₁V₁ = n₁RT₁
We are given:
P₁ = 735 mmHg
V₁ = 745 mL
R = 0.0821 L.atm/mol.K (ideal gas constant)
First, let's convert the pressure and volume to liters and atmospheres:
P₁ = 735 mmHg * (1 atm / 760 mmHg) = 0.967 atm
V₁ = 745 mL * (1 L / 1000 mL) = 0.745 L
Now we can calculate n₁:
0.967 atm * 0.745 L = n₁ * 0.0821 L.atm/mol.K * 298.15 K
0.719 mols = n₁
Step 3: Calculate the final pressure of the flask
When the dry ice sublimes, it will produce carbon dioxide gas. The carbon dioxide gas will occupy the same volume as the original nitrogen gas. Since dry ice is solid carbon dioxide, we can convert its mass to moles and add it to the original number of moles of nitrogen gas.
We are given:
Mass of dry ice = 1.10 g
Molar mass of carbon dioxide (CO₂) = 44.01 g/mol
First, let's convert the mass of dry ice to moles:
1.10 g * (1 mol / 44.01 g) = 0.0250 mol
Now, the total number of moles in the flask after sublimation is:
n_total = n₁ (initial nitrogen gas moles) + n_dryice (moles of dry ice)
n_total = 0.719 mol + 0.0250 mol
n_total = 0.744 mol
Finally, we can use the ideal gas law to calculate the final pressure of the flask:
PV = nRT
P_total * V₁ = n_total * R * T₁
P_total = (n_total * R * T₁) / V₁
P_total = (0.744 mol * 0.0821 L.atm/mol.K * 298.15 K) / 0.745 L
P_total = 21.19 atm
Therefore, the total pressure of the flask is 21.19 atm.
To find the total pressure of the flask, we need to take into account the partial pressure of nitrogen gas and the partial pressure of carbon dioxide gas (resulting from the sublimation of dry ice).
First, let's determine the partial pressure of nitrogen gas. We are given that the flask contains nitrogen gas at a pressure of 735 mm Hg. Therefore, the partial pressure of the nitrogen gas is 735 mm Hg.
Next, let's determine the partial pressure of carbon dioxide gas. When dry ice sublimes, it directly converts from a solid to a gas without passing through the liquid phase. The molar mass of carbon dioxide (CO2) is approximately 44.01 g/mol, and the molar mass of dry ice is also approximately 44.01 g/mol.
We know that 1 mole of an ideal gas occupies 22.4 liters at standard temperature and pressure (STP). Therefore, we can calculate the number of moles of CO2 gas produced by the dry ice using the following conversion:
1.10 g dry ice * (1 mol CO2 / 44.01 g) = 0.025 mol CO2
Now, we need to convert the number of moles of CO2 gas to a partial pressure. We can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the temperature in Kelvin.
We have the volume of the flask, V = 745 mL = 0.745 L, and the temperature in degrees Celsius, T = 25.0 degrees C = 298.15 K.
Substituting the values into the ideal gas law equation for carbon dioxide:
P CO2 * V = (0.025 mol) * (0.0821 L·atm/mol·K) * (298.15 K)
Solving for P CO2 :
P CO2 = (0.025 mol * 0.0821 L·atm/mol·K * 298.15 K) / 0.745 L
P CO2 ≈ 0.8698 atm
Finally, to find the total pressure, we sum up the partial pressures of nitrogen gas and carbon dioxide gas:
Total pressure = P nitrogen gas + P CO2 ≈ 735 mm Hg + 0.8698 atm
Converting the total pressure to the same unit:
Total pressure ≈ 735 mm Hg + (0.8698 atm * 760 mm Hg/atm)
Total pressure ≈ 735 mm Hg + 661.49 mm Hg
Total pressure ≈ 1396.49 mm Hg
Therefore, the total pressure of the flask is approximately 1396.49 mm Hg.