A reaction produced 55.7 mL of nitrogen gas, which was collected over water at 23oC. The measured barometric pressure was 742 torr. If the vapor pressure of water at 23oC is 21 torr, what was the mole fraction of N2 in the collected gas?
Ptotal = PH2O + PN2
You know Ptotal and PH2O, solve for PN2.
Then XN2 = PN2/Ptotal
To determine the mole fraction of N2 in the collected gas, we need to use the partial pressure of nitrogen gas and the total pressure.
First, we need to find the partial pressure of nitrogen gas (PN2). To do this, we subtract the vapor pressure of water (Pwater) from the measured barometric pressure (Ptotal).
PN2 = Ptotal - Pwater
Given:
Ptotal = 742 torr
Pwater = 21 torr
PN2 = 742 torr - 21 torr
PN2 = 721 torr
Now that we have the partial pressure of nitrogen gas, we can calculate the mole fraction (XN2) using the ideal gas law.
The ideal gas law states:
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))
T is the temperature in Kelvin
We can rearrange the ideal gas law to solve for n/V (moles per liter):
n/V = P/RT
Given:
P = PN2 = 721 torr
R = 0.0821 L·atm/(mol·K)
T = 23°C = 23 + 273.15 K = 296.15 K
V = 55.7 mL = 0.0557 L
n/V = 721 torr / (0.0821 L·atm/(mol·K) * 296.15 K)
n/V = 0.0321 mol/L
The mole fraction (XN2) is defined as the moles of N2 divided by the total moles of all gases present in the mixture.
To calculate the mole fraction, we can use the following equation:
XN2 = nN2 / ntotal
Where:
nN2 is the number of moles of nitrogen gas (which is equal to n/V)
ntotal is the number of moles of all gases present in the mixture
We don't have the total moles directly, but since we know that nitrogen gas is the only gas collected, we can assume that ntotal is equal to nN2.
Therefore,
XN2 = nN2 / nN2
XN2 = 1
The mole fraction of N2 in the collected gas is 1.