a 256 mL sample of an unknown gas was collected over water at 23 degrre celsius and 750 mmHg. the gas has a mass of 0.80 grams. what is the molar mass of the gas? (the vapor pressure of water at 23 degree celsius is 21.0 mmHg)
Use PV = nRT and solve for n = number of mols. Then n = grams/molar mass and solve for molar mass.
In the gas equation, for pressure substitute for P = (750-21/760)
Don't forget T must be in kelvin. Volume must be entered in L.
To find the molar mass of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure in atmospheres
V = volume in liters
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature in Kelvin
First, we need to convert the given values to the appropriate units:
Temperature:
23 degrees Celsius = 23 + 273 = 296 Kelvin
Pressure:
Total pressure = 750 mmHg - vapor pressure of water (21.0 mmHg)
Total pressure = 729 mmHg
Convert mmHg to atm: 729 mmHg / 760 mmHg/atm = 0.959 atm
Volume:
256 mL = 256 mL / 1000 L/mL = 0.256 L
Now, we can plug the values into the equation:
(0.959 atm)(0.256 L) = n(0.0821 L·atm/mol·K)(296 K)
Solving for n, the number of moles:
n = (0.959 atm × 0.256 L) / (0.0821 L·atm/mol·K × 296 K)
n = 0.2455 mol
Next, we can calculate the molar mass using the given mass and number of moles:
Molar mass = mass / moles
Molar mass = 0.80 g / 0.2455 mol
Molar mass ≈ 3.26 g/mol
Therefore, the molar mass of the gas is approximately 3.26 g/mol.
To find the molar mass of the gas, we need to use the ideal gas law equation, which is given by:
PV = nRT
Where:
P = Pressure of the gas (corrected for vapor pressure of water)
V = Volume of the gas
n = Number of moles of the gas
R = Ideal gas constant (0.0821 L·atm/(mol·K) or 8.314 J/(mol·K))
T = Temperature in Kelvin
First, let's correct the pressure for the vapor pressure of water. The vapor pressure of water at 23 degrees Celsius is 21.0 mmHg. Therefore, the corrected pressure is:
Corrected Pressure = Total Pressure - Vapor Pressure of Water
Corrected Pressure = 750 mmHg - 21.0 mmHg
Corrected Pressure = 729 mmHg
Next, we need to convert the volume from mL to L and the temperature from Celsius to Kelvin.
Volume = 256 mL = 0.256 L
Temperature = 23 degrees Celsius = 23 + 273 = 296 K
Now, we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = (PV) / (RT)
n = (729 mmHg * 0.256 L) / (0.0821 L·atm/(mol·K) * 296 K)
= (186.624 mmHg·L) / (24.2596 L·mmHg/(mol·K))
≈ 7.6939 mol
Finally, we can calculate the molar mass (M) of the gas using the given mass (m) of the gas and the number of moles (n) we just found:
Molar Mass (M) = Mass (m) / Number of Moles (n)
M = 0.80 g / 7.6939 mol
M ≈ 0.104 g/mol
Therefore, the molar mass of the gas is approximately 0.104 g/mol.