20g of nitrogen gas and 10g of helium gas are placed together in a 5L container at 25C . Calculate the partial pressure of each gas and the total pressure of the gas mixture.
Use PV = nRT and calculate pressure He. Repeat to calculate pressure N2. Add the two for the total pressure.
Find n by n = grams/molar mass
To calculate the partial pressure of each gas and the total pressure of the gas mixture, we can use the ideal gas law equation:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
First, let's calculate the number of moles of each gas:
Number of moles of nitrogen gas (N2):
n(N2) = m/M
where m is the mass of nitrogen gas and M is the molar mass of nitrogen gas.
m(N2) = 20g
M(N2) = 28.02 g/mol
n(N2) = 20g / 28.02 g/mol
n(N2) ≈ 0.713 mol
Number of moles of helium gas (He):
n(He) = m/M
where m is the mass of helium gas and M is the molar mass of helium gas.
m(He) = 10g
M(He) = 4.00 g/mol
n(He) = 10g / 4.00 g/mol
n(He) = 2.5 mol
Now, let's calculate the partial pressure of each gas using the ideal gas law. We will assume the total pressure of the gas mixture is P.
Partial pressure of nitrogen gas (P(N2)):
P(N2) = n(N2)RT/V
Partial pressure of helium gas (P(He)):
P(He) = n(He)RT/V
The total pressure of the gas mixture is the sum of the partial pressures of nitrogen gas and helium gas.
Total pressure of the gas mixture (P(total)):
P(total) = P(N2) + P(He)
Now, let's plug in the values and calculate the pressures.
Given:
V = 5 L
T = 25°C = 25 + 273.15 = 298.15 K
Ideal gas constant (R):
R = 0.0821 L·atm/(mol·K)
Partial pressure of nitrogen gas (P(N2)):
P(N2) = (0.713 mol)(0.0821 L·atm/(mol·K))(298.15 K) / 5 L
P(N2) ≈ 12.72 atm
Partial pressure of helium gas (P(He)):
P(He) = (2.5 mol)(0.0821 L·atm/(mol·K))(298.15 K) / 5 L
P(He) ≈ 37.41 atm
Total pressure of the gas mixture (P(total)):
P(total) = 12.72 atm + 37.41 atm
P(total) ≈ 50.13 atm
Therefore, the partial pressure of nitrogen gas is approximately 12.72 atm, the partial pressure of helium gas is approximately 37.41 atm, and the total pressure of the gas mixture is approximately 50.13 atm.
To calculate the partial pressure of each gas and the total pressure of the gas mixture, you need to use the ideal gas law equation, which is given by:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Ideal gas constant
T = Temperature
Let's break down the steps to calculate the partial pressure and total pressure.
1. Convert the mass of each gas into moles:
To do this, we need to know the molar mass of nitrogen (N2) and helium (He). The molar mass of N2 is 28 g/mol, and the molar mass of He is 4 g/mol.
For nitrogen (N2):
Number of moles = Mass of N2 / Molar mass of N2
Number of moles = 20 g / 28 g/mol
For helium (He):
Number of moles = Mass of He / Molar mass of He
Number of moles = 10 g / 4 g/mol
2. Calculate the total number of moles:
Total number of moles = Moles of N2 + Moles of He
3. Convert the temperature to Kelvin:
Given temperature = 25°C
To convert to Kelvin:
Temperature in Kelvin = Given temperature + 273.15
Temperature in Kelvin = 25 + 273.15
4. Calculate the total pressure:
Total pressure = (Total number of moles) * (Ideal gas constant) * (Temperature in Kelvin) / Volume
5. Calculate the partial pressure of each gas:
Partial pressure of N2 = (Moles of N2) * (Ideal gas constant) * (Temperature in Kelvin) / Volume
Partial pressure of He = (Moles of He) * (Ideal gas constant) * (Temperature in Kelvin) / Volume
Now, let's calculate:
Moles of N2 = 20 g / 28 g/mol = 0.714 mol
Moles of He = 10 g / 4 g/mol = 2.5 mol
Total number of moles = 0.714 mol + 2.5 mol = 3.214 mol
Temperature in Kelvin = 25°C + 273.15 = 298.15 K
Using the ideal gas constant (R) = 0.0821 L·atm/(mol·K):
Total pressure = (3.214 mol) * (0.0821 L·atm/(mol·K)) * (298.15 K) / 5 L
Total pressure ≈ 0.442 atm
Partial pressure of N2 = (0.714 mol) * (0.0821 L·atm/(mol·K)) * (298.15 K) / 5 L
Partial pressure of N2 ≈ 0.0352 atm
Partial pressure of He = (2.5 mol) * (0.0821 L·atm/(mol·K)) * (298.15 K) / 5 L
Partial pressure of He ≈ 0.205 atm
Therefore, the partial pressure of nitrogen gas is approximately 0.0352 atm, the partial pressure of helium gas is approximately 0.205 atm, and the total pressure of the gas mixture is approximately 0.442 atm.