A gas has a density of 1.25 g/L at STP. What is its molecular mass?
33.6
To find the molecular mass of a gas, we need to use the ideal gas law and the molar volume of ideal gases at standard temperature and pressure (STP).
First, let's write down the given information:
Density of the gas at STP = 1.25 g/L
At STP, the conditions are:
Temperature (T) = 273.15 K
Pressure (P) = 1 atm
Molar volume (V) = 22.4 L/mol
The ideal gas law equation is:
PV = nRT
Where:
P = Pressure (in atm)
V = Volume (in L)
n = Number of moles
R = Ideal gas constant (0.0821 L·atm/(mol·K))
T = Temperature (in K)
We can rearrange the equation to solve for the number of moles (n):
n = PV / RT
Now, let's plug in the values:
n = (1 atm)(22.4 L) / (0.0821 L·atm/(mol·K))(273.15 K)
n = 0.0272 mol
The molecular mass of a gas is the mass of one mole of that gas. Therefore, we can calculate the molecular mass by dividing the mass by the number of moles:
Molecular mass = Mass / Moles
Since the density is given in grams per liter (g/L), we can calculate the mass of one liter as follows:
Mass = Density × Volume
Mass = 1.25 g/L × 1 L
Mass = 1.25 g
Now, let's calculate the molecular mass:
Molecular mass = Mass / Moles
Molecular mass = 1.25 g / 0.0272 mol
Molecular mass ≈ 45.96 g/mol
Therefore, the molecular mass of the gas is approximately 45.96 g/mol.
To determine the molecular mass of a gas, we need to use the ideal gas law, which relates the pressure, volume, temperature, and number of moles of a gas.
At STP (Standard Temperature and Pressure), the conditions are defined as follows:
- Temperature = 0 degrees Celsius or 273.15 Kelvin
- Pressure = 1 atmosphere or 101.325 kilopascals
- Volume = 22.4 liters (the molar volume of a gas at STP)
The formula for the ideal gas law is:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
At STP, we can simplify the ideal gas law equation to:
PV = (1 mole)(0.0821 L·atm/mol·K)(273.15 K)
Now, let's calculate the number of moles of the gas.
n = PV / (RT)
= (1.25 g/L) / (0.0821 L·atm/mol·K)(273.15 K)
= 0.045 moles
The molar mass (Molecular mass) of a gas is given by its mass per mole. We can calculate it using the following equation:
Molar mass (Molecular mass) = mass / moles
Given that the density of the gas is 1.25 g/L:
Mass = Density x Volume
Mass = 1.25 g/L x 22.4 L
Mass = 28 g
Now we can calculate the molecular mass of the gas:
Molar mass (Molecular mass) = 28 g / 0.045 moles
Molar mass (Molecular mass) ≈ 622.22 g/mol
Therefore, the molecular mass of the gas is approximately 622.22 g/mol.