Determine the molar mass of a gas with a density of 1.3786 g/L at 80.00 degress celsius and exactly 1 atm.
To determine the molar mass of a gas using its density, we must first calculate the gas's molecular weight using the ideal gas law equation:
PV = nRT
Where:
P = pressure (1 atm)
V = volume (1 L)
n = number of moles
R = ideal gas constant (0.0821 atm L/mol K)
T = temperature in Kelvin (80.00 degrees Celsius = 353.15 K)
Rearranging the equation to solve for the number of moles (n):
n = PV / RT
Substituting the given values:
n = (1 atm) * (1 L) / (0.0821 atm L/mol K * 353.15 K)
n = 0.0291 mol
Now, to calculate the molar mass of the gas, we divide its mass (density) by the number of moles:
Molar mass = Mass / Moles
The given density is 1.3786 g/L, so the mass of the gas in 1 mole is:
Mass = Density * Volume
Mass = 1.3786 g/L * 1 L
Mass = 1.3786 g
Finally, dividing the mass by the number of moles:
Molar mass = 1.3786 g / 0.0291 mol
Molar mass = 47.32 g/mol
Thus, the molar mass of the gas with a density of 1.3786 g/L at 80.00 degrees Celsius and 1 atm is approximately 47.32 g/mol.
To determine the molar mass of a gas, we can use the ideal gas law equation and rearrange it to solve for the molar mass. The ideal gas law is defined as:
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).
In this case, we are given the density of the gas, which can be related to molar mass through the equation:
density = molar mass / molar volume
We can rearrange this equation to solve for molar mass:
molar mass = density × molar volume
First, let's convert the given temperature of 80.00 degrees Celsius to Kelvin:
T (Kelvin) = 80.00 + 273.15 = 353.15 K
Now, we need to calculate the molar volume (V) at the given conditions of pressure, temperature, and density. The molar volume is the volume occupied by one mole of gas:
molar volume = V / n
The molar volume can be calculated using the ideal gas law equation:
PV = nRT
Rearrange the equation to solve for V:
V = nRT / P
Plugging in the known values:
V = (1 mole × 0.0821 L.atm/mol.K × 353.15 K) / (1 atm)
V ≈ 28.94 L/mol
Now, we can substitute the molar volume and density into the equation to find the molar mass:
molar mass = density × molar volume
molar mass = 1.3786 g/L × 28.94 L/mol
molar mass ≈ 39.86 g/mol
Therefore, the molar mass of the gas is approximately 39.86 g/mol.
You can use the gas law of PV = nRT but you must work on that to do it directly.
P*molar mass = density*R*T.
I can show you how you get that equation if you haven't seen it before.