Given that a sample of air is made up of nitrogen, oxygen, and argon in the mole fractions 78% N2, 21% O2, and 1.0% Ar, what is the density at stp?
To find the density of a gas at STP (Standard Temperature and Pressure), we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atmospheres)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L × atm/(mol × K))
T = temperature (in kelvin)
Since we know the mole fractions of the gases, we can assume that we have 100 moles of air. Therefore, we can calculate the number of moles of each gas based on their mole fraction and then sum them up:
Number of moles of N2 = (0.78) * 100 = 78 moles
Number of moles of O2 = (0.21) * 100 = 21 moles
Number of moles of Ar = (0.01) * 100 = 1 mole
Now, we need to convert the moles of each gas to volume using the ideal gas law. Since we want to find the density, we know that density = mass/volume. Therefore, we need to determine the mass of each gas, assuming air has a density of 1.29 g/L at STP.
The molar mass of N2 is 28.014 g/mol, O2 is 31.998 g/mol, and Ar is 39.948 g/mol.
Mass of N2 = number of moles of N2 * molar mass of N2.
Mass of O2 = number of moles of O2 * molar mass of O2.
Mass of Ar = number of moles of Ar * molar mass of Ar.
Now we can use the formula density = mass/volume to find the density of air at STP.
Density = (mass of N2 + mass of O2 + mass of Ar) / total volume.
At STP, the temperature is 273.15 K, and the pressure is 1 atmosphere.
Finally, substitute the values into the equation and calculate the density.
I hope this explanation helps you understand how to calculate the density of air at STP!