A student designs an experiment to determine the molar volume of nitrogen gas using a barometer, thermometer, table of vapor pressures of water, rubber tubing, a container that dispenses nitrogen gas, and a gas collection tube.
a) determine the partial pressure of the nitrogen gas in the collection tube if the total pressure is 1.000 atm and the partial pressure of water is 23.79 torr at 25 degrees C.
b) determine the number of moles of nitrogen gas collected in the tube if the volume of gas collected was 0.0591 L at 25 degrees C
a. Total pressure = pH2O + pgas. Substitute and solve for pN2(the gas).
b. Then PV = nRT.
P is pN2. You know V, R and T. Solve for n.
a) To determine the partial pressure of nitrogen gas in the collection tube, we need to subtract the partial pressure of water vapor from the total pressure. We know that the total pressure is 1.000 atm and the partial pressure of water is 23.79 torr.
First, we need to convert the units of the partial pressure of water vapor from torr to atm.
1 torr = 1 mmHg = 0.00131579 atm (approximately)
So, the partial pressure of water vapor in atm is:
23.79 torr * 0.00131579 atm/torr ≈ 0.03132 atm
Now we can subtract the partial pressure of water vapor from the total pressure:
Partial pressure of nitrogen gas = Total pressure - Partial pressure of water vapor
Partial pressure of nitrogen gas ≈ 1.000 atm - 0.03132 atm ≈ 0.96868 atm
Therefore, the partial pressure of the nitrogen gas in the collection tube is approximately 0.96868 atm.
b) To determine the number of moles of nitrogen gas collected in the tube, we can use the ideal gas law equation: PV = nRT.
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles of gas
R = ideal gas constant = 0.0821 L·atm/(mol·K)
T = temperature (in Kelvin)
First, we need to convert the temperature from degrees Celsius to Kelvin.
Temperature in Kelvin = 25°C + 273.15 ≈ 298.15 K
Now we can rearrange the ideal gas law equation to solve for the number of moles of gas:
n = PV / RT
Plugging in the values we have:
n = (0.96868 atm) * (0.0591 L) / (0.0821 L·atm/(mol·K) * 298.15 K)
Simplifying:
n ≈ 0.01768 mol
Therefore, the number of moles of nitrogen gas collected in the tube is approximately 0.01768 mol.
To determine the molar volume of nitrogen gas, the student needs to perform two calculations:
a) Determine the partial pressure of the nitrogen gas in the collection tube if the total pressure is 1.000 atm and the partial pressure of water is 23.79 torr at 25 degrees C.
To determine the partial pressure of nitrogen gas, we need to subtract the partial pressure of water vapor from the total pressure.
The given total pressure is 1.000 atm, which is equivalent to 760 torr (since 1 atm = 760 torr). And the partial pressure of water vapor is given as 23.79 torr.
To get the partial pressure of nitrogen gas, subtract the partial pressure of water vapor from the total pressure:
Partial pressure of nitrogen gas = Total pressure - Partial pressure of water vapor
= 760 torr - 23.79 torr
= 736.21 torr
Therefore, the partial pressure of nitrogen gas in the collection tube is 736.21 torr.
b) Determine the number of moles of nitrogen gas collected in the tube if the volume of gas collected was 0.0591 L at 25 degrees C.
To determine the number of moles of nitrogen gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature (in Kelvin)
First, convert the temperature from Celsius to Kelvin. Add 273.15 to 25 degrees C to get the temperature in Kelvin:
T = 25 + 273.15
T = 298.15 K
Now, rearrange the ideal gas law equation to solve for moles:
n = PV / RT
Substitute the given values into the equation:
n = (Partial pressure of nitrogen gas) x (Volume of gas collected) / (Ideal gas constant) x (Temperature)
n = (736.21 torr) x (0.0591 L) / (0.0821 L.atm/mol.K) x (298.15 K)
Calculate the value to find the number of moles of nitrogen gas:
n = 0.029647 mol
Therefore, the number of moles of nitrogen gas collected in the tube is approximately 0.029647 mol.