Respuesta :
Answer: The molar composition of nitrogen gas is 0.6 and that of oxygen gas is 0.4
Explanation:
To calculate the molarity of solution, we use the equation:
[tex]\text{Molarity of the solution}=\frac{\text{Mass of solute}}{\text{Molar mass of solute}\times \text{Volume of solution (in L)}}[/tex]
Given mass of nitrogen gas = 51.3 mg = 0.0513 g (Conversion factor: 1 g = 1000 mg)
Molar mass of nitrogen gas = 28 g/mol
Volume of solution = 2 L
Putting values in above equation, we get:
[tex]\text{Molarity of nitrogen gas}=\frac{0.0513g}{28g/mol\times 2L}\\\\\text{Molarity of nitrogen gas}=9.16\times 10^{-4}mol/L[/tex]
To calculate the partial pressure, we use the equation given by Henry's law, which is:
[tex]C_{N_2}=K_H\times p_{N_2}[/tex]
where,
[tex]K_H[/tex] = Henry's constant = [tex]6.1\times 10^{-4}mol/L.atm[/tex]
[tex]C_{N_2}[/tex] = molar solubility of nitrogen gas = [tex]9.16\times 10^{-4}mol/L[/tex]
Putting values in above equation, we get:
[tex]9.16\times 10^{-4}mol/L=6.1\times 10^{-4}mol/L.atm\times p_{N_2}\\\\p_{N_2}=\frac{9.16\times 10^{-4}mol/L}{6.1\times 10^{-4}mol/L.atm}=1.50atm[/tex]
We are given:
Total pressure of the mixture = 2.50 atm
Partial pressure of oxygen gas = 2.50 - 1.50 = 1.00 atm
To calculate the mole fraction of a substance at 25°C, we use the equation given by Raoult's law, which is:
[tex]p_{A}=p_T\times \chi_{A}[/tex] ......(1)
where,
[tex]p_A[/tex] = partial pressure
[tex]p_T[/tex] = total pressure
[tex]\chi_A[/tex] = mole fraction
- For nitrogen gas:
We are given:
[tex]p_{N_2}=1.50atm\\p_T=2.50atm[/tex]
Putting values in equation 1, we get:
[tex]1.50atm=2.50\times \chi_{N_2}\\\\\chi_{N_2}=\frac{1.50}{2.50}=0.6[/tex]
- For oxygen gas:
We are given:
[tex]p_{O_2}=1.00atm\\p_T=2.50atm[/tex]
Putting values in equation 1, we get:
[tex]1.00atm=2.50\times \chi_{O_2}\\\\\chi_{O_2}=\frac{1.00}{2.50}=0.4[/tex]
Hence, the molar composition of nitrogen gas is 0.6 and that of oxygen gas is 0.4
The mole fraction of nitrogen and oxygen is 0.6 and 0.4 respectively.
Data Given;
- Total pressure P = 2.50 atm
- volume of the water = 2.0L
- mass of water = 51.3mg = 0.0513g
- Henry constant for N2 = 6.1*10^-4 M/atm
- Henry constant for O2 = 1.3*10^-3 M/atm
Henry's Law
The law states that the mass of a dissolved gas in a given volume of solvent at equilibrium will be proportional to the partial pressure of the gas.
Mathematically;
C = KP
- c = concentration of the gas
- K = Henry's constant
- P = partial pressure
The number of moles Nitrogen dissolved is
[tex]n = mass/ molar mass\\ n = 0.0513/28\\ n = 0.00183127 moles[/tex]
The concentration of Nitrogen in water is
[tex]\frac{0.00183127}{2} *1 = 0.0009156M[/tex]
Applying Henry's law,
[tex]0.0009156 = 6.1*10^-^4 * P\\ P = 1.5atm[/tex]
The partial pressure of nitrogen in the mixture is 1.5atm
The total pressure of the gas is 2.50atm
Partial Pressure of oxygen = total pressure - partial pressure of nitrogen
partial pressure of oxygen = 2.50 - 1.50 = 1
Pressure Fraction
The pressure fraction of the gas is the ratio between the partial pressure to the total pressure
pressure fraction of nitrogen = 1.5/2.5 = 0.6
pressure fraction of oxygen = 1/2.5 = 0.4
But partial pressure is equal to molar fraction.
This makes the mole fraction of nitrogen equals 0.6 and mole fraction of oxygen equals 0.4.
Learn more about Henry's law here;
https://brainly.com/question/12823901
