A mixture of H2(g) and N2(g) has a density of 0.221 g·L−1 at 301 K and 501 torr. What is the mole fraction composition of the mixture?
find the density of each of H2 and N2 alone
PV=nRT
n=PV/RT=grams/molmass
and then
n/V=grams/(molmass*volume)
so n*molmass=density*molmass
or finaly
density=PV/(molmass*R*T)
Now having density of each H2 and N2
You have the standard mixture problem..
let N be percentN2, and H be percent H2
N*densityN2 + H*densityH2=100*.221g/L
and N+H=100
two equations, two unknowns, solve for N and H
To find the mole fraction composition of the mixture, we need to calculate the number of moles of each gas present and then use those values to determine the mole fractions.
Here's how you can calculate the mole fraction composition of the mixture:
1. First, let's calculate the number of moles of each gas present:
To do this, we need to 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 gas constant, and T is the temperature.
Given:
Density of the mixture (ρ) = 0.221 g·L^−1
Temperature (T) = 301 K
Pressure (P) = 501 torr
We know that the molar mass of H2 is 2 g/mol and the molar mass of N2 is 28 g/mol.
To calculate the number of moles of H2 (n_H2), we need to convert the given density into the molar density (moles per liter). We can use the equation:
Molar Density (mol/L) = Density (g/L) / Molar Mass (g/mol)
The molar density of H2 (n_H2) can be calculated as:
n_H2 = (0.221 g/L) / (2 g/mol) = 0.1105 mol/L
Similarly, for N2:
n_N2 = (0.221 g/L) / (28 g/mol) = 0.0079 mol/L
2. Next, let's calculate the mole fraction of each gas using the following equation:
Mole Fraction (X) = Moles of Gas (n) / Total Moles of Mixture (n_total)
For the mole fraction of H2 (X_H2):
X_H2 = n_H2 / (n_H2 + n_N2)
Substituting the values:
X_H2 = 0.1105 mol/L / (0.1105 mol/L + 0.0079 mol/L)
Calculate X_H2 to get the mole fraction composition of H2.
For the mole fraction of N2 (X_N2):
X_N2 = n_N2 / (n_H2 + n_N2)
Substituting the values:
X_N2 = 0.0079 mol/L / (0.1105 mol/L + 0.0079 mol/L)
Calculate X_N2 to get the mole fraction composition of N2.
Now, plug in the values and calculate the mole fraction composition of H2 and N2 in the mixture.