<u>Answer:</u> The molar mass of unknown diatomic gas is 38 grams
<u>Explanation:</u>
<u>At STP:</u>
The temperature and pressure conditions are 273 K and 1 atm respectively.
To calculate the number of moles, we use the equation given by ideal gas equation:
PV = nRT
P = Pressure of the gas = 1.00 atm
V = Volume of the gas = 12.88 L
n = number of moles of mixture = ?
R = Gas constant = ![0.0821\text{ L atm }mol^{-1}K^{-1}](https://tex.z-dn.net/?f=0.0821%5Ctext%7B%20L%20atm%20%7Dmol%5E%7B-1%7DK%5E%7B-1%7D)
T = Temperature of the gas
Putting values in above equation, we get:
![1.00atm\times 12.88L=n\times 0.0821\text{ L. atm }mol^{-1}K^{-1}\times 273K\\\\n=\frac{1.00\times 12.88}{0.0821\times 273}=0.575mol](https://tex.z-dn.net/?f=1.00atm%5Ctimes%2012.88L%3Dn%5Ctimes%200.0821%5Ctext%7B%20L.%20atm%20%7Dmol%5E%7B-1%7DK%5E%7B-1%7D%5Ctimes%20273K%5C%5C%5C%5Cn%3D%5Cfrac%7B1.00%5Ctimes%2012.88%7D%7B0.0821%5Ctimes%20273%7D%3D0.575mol)
To calculate the number of moles, we use the equation:
.....(1)
Given mass of argon = 5.7 g
Molar mass of argon = 39.95 g/mol
Putting values in equation 1, we get:
![\text{Moles of argon}=\frac{5.7g}{39.95g/mol}=0.143mol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20argon%7D%3D%5Cfrac%7B5.7g%7D%7B39.95g%2Fmol%7D%3D0.143mol)
Given mass of neon = 5.7 g
Molar mass of neon = 20.2 g/mol
Putting values in equation 1, we get:
![\text{Moles of neon}=\frac{5.7g}{20.2g/mol}=0.282mol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20neon%7D%3D%5Cfrac%7B5.7g%7D%7B20.2g%2Fmol%7D%3D0.282mol)
Moles of unknown diatomic gas = [0.575 - (0.143 + 0.282)] = 0.150
Now, calculating the molar mass of unknown diatomic gas from equation 1, we get:
Given mass of unknown diatomic gas = 5.7 g
Moles of unknown diatomic gas = 0.150 moles
Putting values in equation 1, we get:
![0.150mol=\frac{5.7g}{\text{Molar mass of unknown diatomic gas}}\\\\\text{Molar mass of unknown diatomic gas}=\frac{5.7g}{0.150mol}=38g](https://tex.z-dn.net/?f=0.150mol%3D%5Cfrac%7B5.7g%7D%7B%5Ctext%7BMolar%20mass%20of%20unknown%20diatomic%20gas%7D%7D%5C%5C%5C%5C%5Ctext%7BMolar%20mass%20of%20unknown%20diatomic%20gas%7D%3D%5Cfrac%7B5.7g%7D%7B0.150mol%7D%3D38g)
Hence, the molar mass of unknown diatomic gas is 38 grams