To determine the number of atoms in 78.2 liters of Argon, we need to use the ideal gas law and the Avogadro's number. The ideal gas law relates the number of moles of a gas to its volume, pressure, and temperature. Avogadro's number relates the number of moles of a substance to the number of particles (atoms or molecules) in it.
The ideal gas law is:
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.
Rearranging the ideal gas law to solve for n, we get:
n = PV/RT
Avogadro's number is:
NA = 6.022 x 10^23 atoms/mole
To find the number of atoms in 78.2 liters of Argon, we need to know the pressure, temperature, and number of moles of Argon. Let's assume that the pressure and temperature are constant, and use the density of Argon at standard temperature and pressure (STP) to find the number of moles. At STP, the density of Argon is 1.784 g/L.
Converting the volume to liters and the density to grams per liter, we get:
m = ρV = 1.784 g/L x 78.2 L = 139.49 g
To find the number of moles, we divide the mass by the molar mass of Argon, which is 39.95 g/mol:
n = m/M = 139.49 g / 39.95 g/mol ≈ 3.49 mol
Finally, we can find the number of atoms by multiplying the number of moles by Avogadro's number:
N = n x NA = 3.49 mol x 6.022 x 10^23 atoms/mol ≈ 2.10 x 10^24 atoms
Therefore, there are approximately 2.10 x 10^24 atoms in 78.2 liters of Argon.