What is the molar mass of a gas (96.0 g) in a 25.0 L container at 27.0 °C? The pressure inside the container is 3.04E5 Pa.
PV = nRT and solve for n = number of mols.
Then n = grams/molar mass. You know n and grams, solve for molar mass.
To calculate the molar mass of a gas, we'll first need to know the pressure, volume, and temperature of the gas. In this case, we know the pressure (P = 3.04E5 Pa), volume (V = 25.0 L), and temperature (T = 27.0 °C). However, we need to convert the temperature to Kelvin (K).
To convert Celsius to Kelvin, we use the formula:
T(K) = T(°C) + 273.15
Therefore, let's convert the temperature:
T(K) = 27.0 °C + 273.15 = 300.15 K
Now that we have the pressure (P = 3.04E5 Pa), volume (V = 25.0 L), and temperature (T = 300.15 K), we can use the ideal gas law equation to find the number of moles of gas present in the container:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant (8.314 J/(mol·K))
T = temperature
Rearranging the equation to solve for n, the number of moles, we get:
n = PV / RT
Now let's substitute the values into the equation to find the number of moles:
n = (3.04E5 Pa) * (25.0 L) / [(8.314 J/(mol·K)) * (300.15 K)]
Simplifying the equation gives us:
n ≈ 96.39 mol
Therefore, the number of moles of gas in the container is approximately 96.39 mol.
Next, to calculate the molar mass of the gas, we'll divide the mass of the gas (96.0 g) by the number of moles (96.39 mol):
Molar mass = mass / number of moles
Molar mass = 96.0 g / 96.39 mol
Simplifying the equation gives us:
Molar mass ≈ 0.995 g/mol
Therefore, the molar mass of the gas is approximately 0.995 g/mol.