To calculate the number of argon atoms in 1.00 L of the sample, we need to use Avogadro's law and the ideal gas law.
Avogadro's law states that equal volumes of gases at the same temperature and pressure contain the same number of molecules.
The ideal gas law is given by the equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant (0.0821 L·atm/(mol·K)), and T is the temperature in Kelvin.
At STP (standard temperature and pressure), the temperature is 273.15 K and the pressure is 1 atm.
First, let's find the number of moles of argon in 5.51 L of the sample using the ideal gas law:
PV = nRT
(1 atm) (5.51 L) = n (0.0821 L·atm/(mol·K)) (273.15 K)
5.51 = n(0.0821)(273.15)
n = 0.206 mol
Now, we can use Avogadro's law to find the number of argon atoms:
1 L / 5.51 L = x atoms / 0.206 mol
x = (1 L / 5.51 L) * (0.206 mol)
x = 0.0373 mol
Finally, we can convert the number of moles to the number of argon atoms using Avogadro's number. Avogadro's number is approximately 6.022 × 10^23 atoms/mol.
Number of argon atoms = (0.0373 mol) * (6.022 × 10^23 atoms/mol)
Number of argon atoms = 2.245 × 10^22 atoms
Therefore, there are approximately 2.245 × 10^22 argon atoms in 1.00 L of the sample.
Now let's calculate the mass of 3.01 * 10^22 formula units of calcium carbonate.
The molar mass of calcium carbonate (CaCO3) is calculated as follows:
Ca: 40.08 g/mol
C: 12.01 g/mol
O: 16.00 g/mol (there are three oxygen atoms in calcium carbonate)
Molar mass of CaCO3: (40.08 g/mol) + (12.01 g/mol) + (16.00 g/mol * 3) = 100.09 g/mol
To find the mass of 3.01 * 10^22 formula units of calcium carbonate, we can use the following calculation:
Mass = (3.01 * 10^22) * (100.09 g/mol)
Mass = 3.01309 * 10^24 g
The mass of 3.01 * 10^22 formula units of calcium carbonate is approximately 3.01309 * 10^24 grams.