Calculate the molecular weight of a gas if 16.8 g of the gas occupies 16.3 L at STP.
mols of the gas = 16.3/22.4 = ?
Then mols = g/molar mass. You know mols and grams, solve for molar mass.
To calculate the molecular weight of a gas, we need to use the Ideal Gas Law equation, which relates the pressure, volume, temperature, and number of moles of a gas.
The formula for the Ideal Gas Law is:
PV = nRT
Where:
P is the pressure of the gas (in atm)
V is the volume of the gas (in liters)
n is the number of moles of the gas
R is the ideal gas constant (0.0821 L.atm/mol.K)
T is the temperature of the gas (in Kelvin)
At STP (Standard Temperature and Pressure):
- The temperature is 273.15 Kelvin (0 degrees Celsius)
- The pressure is 1 atm (atmosphere)
Now, let's solve for the number of moles (n) of the gas using the provided data:
P = 1 atm
V = 16.3 L
R = 0.0821 L.atm/mol.K
T = 273.15 K
Plugging in the values into the formula:
(1 atm) x (16.3 L) = n x (0.0821 L.atm/mol.K) x (273.15 K)
Rearranging the equation to solve for n:
n = (1 atm x 16.3 L) / (0.0821 L.atm/mol.K x 273.15 K)
n = (16.3 atm.L) / (22.414 L/mol) [Note: 0.0821 L.atm/mol.K x 273.15 K is equal to 22.414 L/mol, which is the molar volume at STP.]
n ≈ 0.729 mol
Now that we have the number of moles (n = 0.729 mol) and the mass of the gas (16.8 g), we can calculate the molecular weight (M) using the equation:
M = mass / moles
M = 16.8 g / 0.729 mol
M ≈ 23.05 g/mol
Therefore, the molecular weight of the gas is approximately 23.05 g/mol.