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 find the number of moles in a gas sample, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = gas constant (0.0821 L.atm/mol.K)
T = temperature (in Kelvin)
Let's calculate the number of moles first:
Given:
Pressure (P) = 2.1 atm
Volume (V) = 30.0 L
Temperature (T) = 298 K
Using the ideal gas law equation:
n = PV / RT
n = (2.1 atm * 30.0 L) / (0.0821 L.atm/mol.K * 298 K)
n = 2.1 * 30.0 / 0.0821 * 298
n ≈ 2.54 moles
So, the gas sample contains approximately 2.54 moles.
To calculate the mass of the gas, we'll need to know the molar mass of the gas.
The molar mass of helium (He) is approximately 4.00 g/mol.
The molar mass of argon (Ar) is approximately 39.95 g/mol.
To find the mass of the gas sample, we multiply the number of moles by the molar mass.
For helium (He):
Mass of He = number of moles * molar mass of He
Mass of He = 2.54 moles * 4.00 g/mol
Mass of He ≈ 10.16 grams
For argon (Ar):
Mass of Ar = number of moles * molar mass of Ar
Mass of Ar = 2.54 moles * 39.95 g/mol
Mass of Ar ≈ 101.57 grams
Therefore, if the gas is helium, the mass of the gas sample is approximately 10.16 grams. If the gas is argon, the mass is approximately 101.57 grams.
To find the number of moles, we can use the ideal gas law:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
First, let's calculate the number of moles. We know:
P = 2.1 ATM
V = 30.0 L
T = 298 K
R = 0.0821 L·atm/(mol·K) (ideal gas constant)
Using the formula PV = nRT, we can solve for n:
n = (PV) / (RT)
Substituting the given values:
n = (2.1 ATM * 30.0 L) / (0.0821 L·atm/(mol·K) * 298 K)
Calculating this:
n ≈ 2.79 moles
Therefore, the sample contains approximately 2.79 moles of gas.
Now, let's calculate the mass of the gas if it is helium (He). The molar mass of helium is approximately 4 g/mol.
To find the mass, we can use the formula:
mass = number of moles * molar mass
Substituting the values:
mass = 2.79 moles * 4 g/mol
Calculating this:
mass ≈ 11.16 g
So, if the gas is helium, the mass of the gas is approximately 11.16 grams.
Next, let's calculate the mass of the gas if it is argon (Ar). The molar mass of argon is approximately 40 g/mol.
Using the same formula:
mass = number of moles * molar mass
Substituting the values:
mass = 2.79 moles * 40 g/mol
Calculating this:
mass ≈ 111.6 g
Therefore, if the gas is argon, the mass of the gas is approximately 111.6 grams.