The theoritical yeild of a reaction that gives off nitrogen trifluoride gas is 844 mL at STP. What total volume of NF3 plus water vapor will be collected over water at 25° C and a total pressure of 1.017 atm?
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To solve this problem, we need to use the ideal gas law and Dalton's law of partial pressures.
Step 1: Convert the given conditions to Kelvin temperature.
Temperature in °C = 25 °C
Temperature in Kelvin = 25 + 273 = 298 K
Step 2: Calculate the partial pressure of water vapor at 25 °C.
According to the water vapor pressure table, at 25 °C the partial pressure of water vapor is 23.76 mmHg.
Step 3: Convert the partial pressure of water vapor from mmHg to atm.
1 atm = 760 mmHg
Partial pressure of water vapor = 23.76 mmHg/760 mmHg/atm = 0.031 atm
Step 4: Calculate the partial pressure of the nitrogen trifluoride gas.
Total pressure - partial pressure of water vapor = partial pressure of nitrogen trifluoride gas
Partial pressure of nitrogen trifluoride gas = 1.017 atm - 0.031 atm = 0.986 atm
Step 5: Use the ideal gas law to calculate the volume of nitrogen trifluoride gas.
PV = nRT
Where:
P = partial pressure of nitrogen trifluoride gas (0.986 atm)
V = volume of nitrogen trifluoride gas
n = number of moles of nitrogen trifluoride gas (to be calculated)
R = gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin (298 K)
Rearranging the equation and solving for V:
V = nRT / P
V = (844 mL / 1000 mL/L) * (0.0821 L·atm/(mol·K)) * (298 K) / (0.986 atm)
V = 20.828 mol
Step 6: Now, we need to convert the moles of nitrogen trifluoride gas to volume.
Using the ideal gas law again:
V = nRT / P
V = (20.828 mol) * (0.0821 L·atm/(mol·K)) * (298 K) / (0.986 atm)
V = 506.81 L
Step 7: Since we collected the gas over water, we need to subtract the water vapor's volume.
Total volume of NF3 plus water vapor = Volume of nitrogen trifluoride gas - Volume of water vapor
Total volume = 506.81 L - 0.844 L
Total volume = 505.966 L
Therefore, the total volume of NF3 plus water vapor collected over water at 25 °C and a total pressure of 1.017 atm is approximately 505.966 L.
To determine the total volume of NF3 plus water vapor collected over water at a given temperature and pressure, we need to consider the ideal gas law and the concept of partial pressure.
Given:
The theoretical yield of NF3 gas at STP (standard temperature and pressure) is 844 mL.
We have the following conditions:
- Temperature: 25°C (convert to Kelvin: 25°C + 273.15 = 298.15 K)
- Total pressure: 1.017 atm
First, let's convert the volume from mL to liters:
844 mL = 0.844 L
Next, let's calculate the partial pressure of NF3 gas. Since it is the only gas mentioned, the partial pressure of NF3 is equal to the total pressure:
Partial pressure of NF3 (P(NF3)) = Total pressure = 1.017 atm
Now, we need to use the ideal gas law equation with the partial pressure of NF3 to determine the moles of NF3:
PV = nRT
Where:
P = partial pressure of NF3 in atm
V = volume of NF3 in L
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature in Kelvin
Rearranging the equation, we get:
n = PV / RT
Plugging in the values, we have:
n = (1.017 atm * 0.844 L) / (0.0821 L.atm/mol.K * 298.15 K)
Calculating this, we find the number of moles of NF3.
Next, we consider the water vapor. At the given temperature and pressure, water is in the gas phase, so we need to account for its partial pressure.
To find the partial pressure of water vapor at 25°C, we can consult a vapor pressure table or use a calculator. At 25°C, the vapor pressure of water is approximately 23.756 mmHg or 0.031 atm.
Therefore, the partial pressure of water vapor (P(H2O)) = 0.031 atm.
Now, we can determine the total pressure of the mixture:
Total pressure = Partial pressure of NF3 + Partial pressure of water vapor
total pressure = 1.017 atm + 0.031 atm
Finally, using the ideal gas law once more, we can solve for the total volume:
V = nRT / P
Plugging in the appropriate values, we can calculate the total volume of NF3 plus water vapor collected over water at the given conditions.
Subtract the vapor pressure of water from total pressure, that yields the partial pressure of the gas.
Now you have temp, partial pressure, use the combined gas law to find the new volume.