Density : <u>0.01229 g/ml</u>
Molar mass : <u>31.525 g/mol</u>
<h3>Further explanation
</h3>
Some of the laws regarding gas, can apply to ideal gas (volume expansion does not occur when the gas is heated),:
- Boyle's law at constant T, P = 1 / V
- Charles's law, at constant P, V = T
- Avogadro's law, at constant P and T, V = n
So that the three laws can be combined into a single gas equation, the ideal gas equation
In general, the gas equation can be written
where
P = pressure, atm
V = volume, liter
n = number of moles
R = gas constant = 0.08206 L.atm / mol K
T = temperature, Kelvin
Density is a quantity derived from the mass and volume
density is the ratio of mass per unit volume
The unit of density can be expressed in g / cm3 or kg / m3
Density formula:
![\large {\boxed {\bold {\rho ~ = ~ \frac {m} {V}}}}](https://tex.z-dn.net/?f=%5Clarge%20%7B%5Cboxed%20%7B%5Cbold%20%7B%5Crho%20~%20%3D%20~%20%5Cfrac%20%7Bm%7D%20%7BV%7D%7D%7D%7D)
ρ = density
m = mass
v = volume
2.15 g of an unknown gas at 71 degrees C and 1.10 atm is stored in a 1.75 L flask.
so density = mass : volume
![\rm density=\rho=\dfrac{21.5}{1750}=\boxed{0.01229\dfrac{g}{ml}}](https://tex.z-dn.net/?f=%5Crm%20density%3D%5Crho%3D%5Cdfrac%7B21.5%7D%7B1750%7D%3D%5Cboxed%7B0.01229%5Cdfrac%7Bg%7D%7Bml%7D%7D)
To find the molar mass, we first look for the number of moles with the ideal gas equation:
PV = nRT
T = 71 °C + 273 = 344 K
![\rm n=\dfrac{PV}{RT}\\\\n=\dfrac{1.10\times 1.75}{0.08206\times 344}\\\\n=\boxed{0.0682}](https://tex.z-dn.net/?f=%5Crm%20n%3D%5Cdfrac%7BPV%7D%7BRT%7D%5C%5C%5C%5Cn%3D%5Cdfrac%7B1.10%5Ctimes%201.75%7D%7B0.08206%5Ctimes%20344%7D%5C%5C%5C%5Cn%3D%5Cboxed%7B0.0682%7D)
![\rm molar\:mass=\dfrac{mass}{mol}\\\\molar~mass=\frac{2.15}{0.0682}\\\\molar\:mass=\boxed{\bold{31.525\:\dfrac{g}{mol} }}](https://tex.z-dn.net/?f=%5Crm%20molar%5C%3Amass%3D%5Cdfrac%7Bmass%7D%7Bmol%7D%5C%5C%5C%5Cmolar~mass%3D%5Cfrac%7B2.15%7D%7B0.0682%7D%5C%5C%5C%5Cmolar%5C%3Amass%3D%5Cboxed%7B%5Cbold%7B31.525%5C%3A%5Cdfrac%7Bg%7D%7Bmol%7D%20%7D%7D)
<h3>Learn more
</h3>
Which equation agrees with the ideal gas law
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Which law relates to the ideal gas law
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