A gas weighing 23.6 g occupies a 10.0 L flask at 27 C and 780. torr of pressure. Calculate the molar mass of the gas.
Use PV = nRT and solve for n = mols gas.
Then n = grams/molar mass. You know grams and n, solve for molar mass.
To calculate the molar mass of the gas, we can use the ideal gas law equation:
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 Kelvin
First, convert the given pressure to atm:
780. torr / 760. torr/atm = 1.03 atm
Next, convert the temperature to Kelvin:
27 C + 273 = 300 K
Rearrange the ideal gas law equation to solve for n:
n = (PV) / (RT)
n = (1.03 atm * 10.0 L) / (0.0821 L.atm/(mol.K) * 300 K)
n = 0.410 mol
Now, we'll calculate the molar mass using the formula:
Molar mass = mass / amount of substance
Molar mass = 23.6 g / 0.410 mol
Molar mass = 57.6 g/mol
Therefore, the molar mass of the gas is 57.6 g/mol.
To calculate the molar mass of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas (in atm)
V = volume of the gas (in L)
n = number of moles of the gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature of the gas (in Kelvin)
First, we need to convert the given values to the appropriate units.
Pressure: 780. torr = 780. / 760. = 1.026 atm
Volume: 10.0 L
Temperature: 27°C = 27 + 273.15 = 300.15 K
Now, we rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
Substituting the values in, we have:
n = (1.026 atm)(10.0 L) / (0.0821 L·atm/(mol·K))(300.15 K)
Calculating this value gives us:
n = 0.4247 mol
Next, we can calculate the molar mass of the gas using the equation:
Molar mass = mass (in grams) / number of moles
Given that the gas weighs 23.6 g, we divide it by the number of moles calculated earlier:
Molar mass = 23.6 g / 0.4247 mol
Calculating this gives us:
Molar mass ≈ 55.57 g/mol
So, the molar mass of the gas is approximately 55.57 g/mol.