A sample of gas has a mass of 0.565g . Its volume is 120 mL at a temperature of 80∘C and a pressure of 747 mmHg . what is the molar mass
Use PV = nRT and solve for n = number of mols, then n = grams/molar mass. You know n and grams, solve for molar mass.
To find the molar mass of a gas, you can use the ideal gas law formula:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Ideal gas constant (0.0821 L·atm/(mol·K))
T = Temperature (in Kelvin)
First, let's convert the given values to the correct units:
- Temperature: 80∘C = 273 + 80 = 353 K
- Volume: 120 mL = 120/1000 = 0.12 L
- Pressure: 747 mmHg
Now, let's rearrange the ideal gas law formula to solve for n (number of moles):
n = (PV) / (RT)
Substituting the given values:
n = (747 mmHg * 0.12 L) / (0.0821 L·atm/(mol·K) * 353 K)
Simplifying the equation:
n = (89.64 mmHg * L) / (28.913 L·mmHg/(mol·K))
Canceling out units:
n = 89.64 mol/mol·K
Finally, to find the molar mass, divide the mass of the gas by the number of moles:
Molar mass = mass / moles
Molar mass = 0.565 g / 89.64 mol/mol·K
Molar mass = 0.0063 g/mol·K
Therefore, the molar mass of the gas is approximately 0.0063 g/mol·K.