A 0.0097561 g quantity of an unknown gas occupies 0.2 L at 500 K and 2 atm. What is the Molecular Weight (MW) of the gas ?
Use PV = nRT and solve for n = moles. Then n = grams/molecular weight. Solve for MW.
To find the molecular weight (MW) of the gas, we need to use the ideal gas law equation:
PV = nRT
Where:
P = Pressure (in atm)
V = Volume (in liters)
n = Number of moles
R = Ideal gas constant (0.0821 L·atm/mol·K)
T = Temperature (in Kelvin)
First, let's convert the given data into the proper units:
Mass = 0.0097561 g
Volume = 0.2 L
Pressure = 2 atm
Temperature = 500 K
Next, we need to calculate the number of moles (n) of the gas using the formula:
n = Mass / Molecular weight
Rearrange the formula to solve for Molecular weight (MW):
MW = Mass / n
Now, let's calculate the number of moles (n) using the ideal gas law equation:
PV = nRT
n = PV / RT
Substituting the given values:
n = (2 atm * 0.2 L) / (0.0821 L·atm/mol·K * 500 K)
Simplifying:
n = 0.040 L·atm / (0.0821 L·atm/mol·K * 500 K)
n ≈ 0.000972 mol
Now, we can substitute the value of n into the formula to find the Molecular Weight (MW):
MW = Mass / n
MW ≈ 0.0097561 g / 0.000972 mol
MW ≈ 10.04 g/mol
Therefore, the molecular weight (MW) of the gas is approximately 10.04 g/mol.