Respuesta :
Answer: The molar mass of unknown diatomic gas is 38 grams
Explanation:
At STP:
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 = [tex]0.0821\text{ L atm }mol^{-1}K^{-1}[/tex]
T = Temperature of the gas
Putting values in above equation, we get:
[tex]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[/tex]
To calculate the number of moles, we use the equation:
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex] .....(1)
- For Argon:
Given mass of argon = 5.7 g
Molar mass of argon = 39.95 g/mol
Putting values in equation 1, we get:
[tex]\text{Moles of argon}=\frac{5.7g}{39.95g/mol}=0.143mol[/tex]
- For neon:
Given mass of neon = 5.7 g
Molar mass of neon = 20.2 g/mol
Putting values in equation 1, we get:
[tex]\text{Moles of neon}=\frac{5.7g}{20.2g/mol}=0.282mol[/tex]
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:
[tex]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[/tex]
Hence, the molar mass of unknown diatomic gas is 38 grams
