To find the molar mass of the unknown gas, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure (at STP, the pressure is 1 atm)
V = volume (14.30 L)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (at STP, the temperature is 273.15 K)
First, let's determine the number of moles of argon (Ar), neon (Ne), and the unknown gas present in the mixture.
For argon:
The molar mass of Ar is 39.95 g/mol
The number of moles of Ar can be calculated using the formula:
number of moles = mass / molar mass
number of moles of Ar = 7.2 g / 39.95 g/mol = 0.18045 mol
For neon:
The molar mass of Ne is 20.18 g/mol
The number of moles of Ne can be calculated using the formula:
number of moles = mass / molar mass
number of moles of Ne = 7.2 g / 20.18 g/mol = 0.35676 mol
To find the number of moles of the unknown gas, we subtract the moles of argon and neon from the total moles of the mixture:
Number of moles of the unknown gas = Total moles - moles of Ar - moles of Ne
Total moles = moles of Ar + moles of Ne
Total moles = 0.18045 mol + 0.35676 mol = 0.53721 mol
Number of moles of the unknown gas = 0.53721 mol - 0.18045 mol - 0.35676 mol = 0.0 mol
Since the number of moles of the unknown gas is zero, it means that there is no unknown gas present in the mixture. Therefore, the molar mass of the unknown gas cannot be determined, and the identity of the unknown gas is unknown.