1. Convert Temperature to Kelvin
* T (Kelvin) = T (Celsius) + 273.15
* T = 20°C + 273.15 = 293.15 K
2. Use the Ideal Gas Law
* PV = nRT
* P = pressure (atm) = 0.090 atm
* V = volume (L) = 1.8 L
* n = moles of gas (mol)
* R = ideal gas constant = 0.0821 L·atm/mol·K
* T = temperature (K) = 293.15 K
3. Solve for Moles (n)
* n = (PV) / (RT)
* n = (0.090 atm * 1.8 L) / (0.0821 L·atm/mol·K * 293.15 K)
* n ≈ 0.067 mol
4. Calculate Molar Mass
* Molar mass = mass (g) / moles (mol)
* Molar mass = 589 g / 0.067 mol
* Molar mass ≈ 8800 g/mol
Therefore, the molar mass of the unknown gas is approximately 8800 g/mol.
Important Note: This calculation assumes the gas behaves ideally. In reality, gases may deviate from ideal behavior at high pressures or low temperatures.
