A mixture contains 5.00 g each of O2, N2, CO2, and Ne gas. Calculate the volume of this mixture at STP. Calculate the partial pressure of each gas in the mixture at STP.
Hairy blls
Convert 5.00 g each gas to moles. moles = grams/molar mass
Use PV = nRT to calculate volume at STP using total n.
Calculate mole fraction of each gas.
Pgas = XgasPtotal.
To calculate the volume of the gas mixture at STP, we need to 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)
At STP (Standard Temperature and Pressure):
Temperature (T) = 273 K
Pressure (P) = 1 atm
First, let's calculate the number of moles for each gas in the mixture:
To calculate the number of moles, we will use the formula:
n = mass / molar mass
The molar mass of each gas is as follows:
O2: 32.00 g/mol
N2: 28.02 g/mol
CO2: 44.01 g/mol
Ne: 20.18 g/mol
Therefore, the number of moles for each gas in the mixture is:
n(O2) = 5.00 g / 32.00 g/mol = 0.15625 mol
n(N2) = 5.00 g / 28.02 g/mol = 0.17825 mol
n(CO2) = 5.00 g / 44.01 g/mol = 0.11359 mol
n(Ne) = 5.00 g / 20.18 g/mol = 0.24757 mol
Now, let's calculate the total number of moles for the mixture:
Total Moles = n(O2) + n(N2) + n(CO2) + n(Ne)
= 0.15625 mol + 0.17825 mol + 0.11359 mol + 0.24757 mol
= 0.69566 mol
To find the volume, we rearrange the ideal gas law equation:
V = nRT / P
V = (0.69566 mol) * (0.0821 L·atm/mol·K) * (273 K) / (1 atm)
V ≈ 15.82 L
So, the volume of the gas mixture at STP is approximately 15.82 liters.
Now let's calculate the partial pressure of each gas in the mixture at STP. At STP, the total pressure is 1 atm.
Partial pressure of O2 (P(O2)) = n(O2) * P(total)
= 0.15625 mol * 1 atm
= 0.15625 atm
Partial pressure of N2 (P(N2)) = n(N2) * P(total)
= 0.17825 mol * 1 atm
= 0.17825 atm
Partial pressure of CO2 (P(CO2)) = n(CO2) * P(total)
= 0.11359 mol * 1 atm
= 0.11359 atm
Partial pressure of Ne (P(Ne)) = n(Ne) * P(total)
= 0.24757 mol * 1 atm
= 0.24757 atm
Therefore, the partial pressure of O2 is 0.15625 atm, N2 is 0.17825 atm, CO2 is 0.11359 atm, and Ne is 0.24757 atm in the mixture at STP.