Answer :
To find the molar mass of the gaseous compound, we need to use the ideal gas law equation:
PV = nRT
where P is the pressure (1.62 atm), V is the volume (1 L, since the density is given in g/L), n is the number of moles, R is the gas constant (0.0821 L atm/mol K), and T is the temperature in Kelvin (296.65 K, since 23.5°C = 296.65 K).
First, we need to find the number of moles of the gas:
n = PV/RT
n = (1.62 atm)(1 L)/(0.0821 L atm/mol K)(296.65 K)
n = 0.0653 mol
Next, we can use the definition of molar mass (mass per mole) to find the molar mass of the gas:
Molar mass = mass/number of moles
Since we know the density of the gas (1.64 g/L), we can use it to find the mass of 1 mole of the gas:
mass = density x volume = 1.64 g/L x 1 L = 1.64 g
Therefore, the molar mass of the gas is:
Molar mass = mass/number of moles = 1.64 g/0.0653 mol = 25.1 g/mol
So the molar mass of the gaseous compound is approximately 25.1 g/mol.
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