7.34 grams of a gas occupies a volume of 2.5 liters at a pressure of 1216. mm and a temperature of 73 degrees celsius. What is the molecular weight of the gas?
PV = nRT and solve for n = number of mols. Then n = g/molar mass. You have g and n, solve for molar mass.
To determine the molecular weight of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature in Kelvin
First, we need to convert the given values to the appropriate units.
Given:
Mass of gas (m) = 7.34 grams
Volume (V) = 2.5 liters
Pressure (P) = 1216 mm
We need to convert pressure from mm to atm:
1 atm = 760 mmHg
1 mmHg = 1 torr
1 atm = 1013.25 mmHg
Therefore, pressure (P) = 1216 mmHg / 1013.25 mmHg/atm ≈ 1.2 atm
Temperature (T) = 73 degrees Celsius
To convert temperature from Celsius to Kelvin, we add 273.15:
T = 73 + 273.15 = 346.15 K
Now, we rearrange the ideal gas law equation to solve for the number of moles:
n = PV / RT
n = (1.2 atm) * (2.5 L) / [(0.0821 L·atm/(mol·K)) * (346.15 K)]
Using the values above, we can calculate the number of moles (n).
n ≈ 0.135 moles
Finally, to find the molecular weight of the gas, we can use the equation:
Molecular weight = Mass / Moles
Molecular weight = 7.34 g / 0.135 moles
Molecular weight ≈ 54.37 g/mol
Therefore, the molecular weight of the gas is approximately 54.37 grams per mole.