An unknown amount of gas occupies 30.0 L at 2.1 atm and 298K. How many moles does the sample contain? What is the mass if the gas is helium? What is the mass if the gas is argon?
To determine the number of moles in a gas sample, we can use the ideal gas law equation:
PV = nRT,
where P represents pressure, V represents volume, n represents the number of moles, R is the ideal gas constant, and T signifies temperature.
1. Number of moles:
Given:
Pressure (P) = 2.1 atm
Volume (V) = 30.0 L
Temperature (T) = 298 K
First, we need to convert the pressure to units of Pascal (Pa). Since 1 atm = 101325 Pa:
Pressure (P) = 2.1 atm × 101325 Pa/atm = 211,841.25 Pa
Next, we need to convert the volume to units of cubic meters (m^3). Since 1 L = 0.001 m^3:
Volume (V) = 30.0 L × 0.001 m^3/L = 0.03 m^3
The gas constant (R) is 8.314 J/(mol·K).
Now we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
n = (211841.25 Pa) × (0.03 m^3) / (8.314 J/(mol·K) × 298K)
n ≈ 2.52 moles (rounded to two decimal places)
Therefore, the gas sample contains approximately 2.52 moles.
2. Mass of the gas sample if it is helium:
The molar mass of helium (He) is approximately 4.0026 g/mol.
To calculate the mass of the gas sample, we can use the equation:
Mass = Number of moles × Molar mass
Mass = 2.52 moles × 4.0026 g/mol
Mass ≈ 10.08 g (rounded to two decimal places)
If the gas is helium, the mass of the sample is approximately 10.08 grams.
3. Mass of the gas sample if it is argon:
The molar mass of argon (Ar) is approximately 39.948 g/mol.
To calculate the mass of the gas sample, we use the same equation:
Mass = Number of moles × Molar mass
Mass = 2.52 moles × 39.948 g/mol
Mass ≈ 100.55 g (rounded to two decimal places)
If the gas is argon, the mass of the sample is approximately 100.55 grams.