3.15 g of an unknown gas at 53 °C and 1.00 atm is stored in a 1.55-L flask. The gas has a density of 2.03 g/L. What is the molar mass of the gas?
You can rework the PV = nRT equation to P*molar mass = density*RT and solve for molar mass.
To find the molar mass of the gas, we need to use the formula:
Molar mass = (mass of gas) / (number of moles of gas)
First, let's find the number of moles of the gas. We can use the ideal gas law equation to determine this:
PV = nRT
Where:
P = pressure (1.00 atm)
V = volume (1.55 L)
n = number of moles (unknown)
R = ideal gas constant (0.0821 L•atm/mol•K)
T = temperature (53 °C = 326 K)
Rearranging the formula to solve for n:
n = (PV) / (RT)
Substituting the given values:
n = (1.00 atm * 1.55 L) / (0.0821 L•atm/mol•K * 326 K)
Calculating this will give us the number of moles of the gas.
Next, we can calculate the mass of the gas using the density:
Mass = density * volume
Substituting the given values:
Mass = 2.03 g/L * 1.55 L
Calculating this will give us the mass of the gas.
Now we have both the mass and number of moles of the gas. We can substitute these values into the formula to find the molar mass:
Molar mass = mass of gas / number of moles of gas
Calculating this will give us the molar mass of the gas.