A sample of unknown gas weighs 2.96 g and occupies 750. mL at 760. mmHg and 100.°C. What is the molar mass of the unknown gas?
Use PV = nRT and solve for n = number of mols.
Then n = grams/molar mass. Solve for molar mass
To find the molar mass of the unknown gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas (in this case, it is given as 760. mmHg)
V = volume of the gas (in this case, it is given as 750. mL)
n = number of moles of the gas (which we need to find)
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature of the gas in Kelvin (in this case, it is given as 100°C)
First, we need to convert the given values to the appropriate units:
- Convert the pressure from mmHg to atm: 760. mmHg / 760 = 1 atm
- Convert the volume from mL to L: 750. mL / 1000 = 0.75 L
- Convert the temperature from Celsius to Kelvin: 100°C + 273.15 = 373.15 K
Now we can rearrange the ideal gas law equation to solve for the number of moles (n) of the gas:
n = (PV) / (RT)
Plugging in the values we obtained:
n = (1 atm * 0.75 L) / (0.0821 L·atm/(mol·K) * 373.15 K)
Simplifying:
n = 0.00924 mol
Now that we have the number of moles (n), we can calculate the molar mass of the unknown gas.
Molar mass = (mass of the gas) / (number of moles)
Plugging in the given mass: 2.96 g, and the calculated number of moles: 0.00924 mol
Molar mass = 2.96 g / 0.00924 mol
The molar mass of the unknown gas is approximately 319.79 g/mol.