Taking into account the definition of density and ideal gas law, the density of aluminum chloride vapor (AlCl₃) at 498 K and 0.939 atm is 3.06 g/L.
Density is defined as the property that matter, whether solid, liquid or gas, has to compress into a given space.
In other words, density is a quantity that allows us to measure the amount of mass in a certain volume of a substance. Then, the expression for the calculation of density is the quotient between the mass of a body and the volume it occupies:
[tex]density=\frac{mass}{volume}[/tex]
Ideal gases are a simplification of real gases that is done to study them more easily. It is considered to be formed by point particles, do not interact with each other and move randomly. It is also considered that the molecules of an ideal gas, in themselves, do not occupy any volume.
An ideal gas is characterized by three state variables: absolute pressure (P), volume (V), and absolute temperature (T). The relationship between them constitutes the ideal gas law, an equation that relates the three variables if the amount of substance, number of moles n, remains constant and where R is the molar constant of gases:
P×V = n×R×T
From the Ideal gas law, you can get that:
[tex]\frac{n}{V} =\frac{P}{RxT}[/tex]
On the other side, the molar mass of substance is a property defined as the amount of mass that a substance contains in one mole. It can be expressed as:
[tex]molar mass= \frac{mass}{number of moles}[/tex]
Then, the number of moles n can be calculated as:
[tex]n=\frac{mass}{molar mass}[/tex]
So:
[tex]\frac{\frac{mass}{molar mass} }{V} =\frac{P}{RxT}[/tex]
Solving you get the expression:
[tex]\frac{mass }{V} =\frac{Pxmolar mass}{RxT}[/tex]
Considering the definition of density, you finally get:
[tex]density=\frac{Pxmolar mass}{RxT}[/tex]
In this case, you know:
Replacing in the previous expression for the calculation of the density:
[tex]density=\frac{0.939 atmx133.35\frac{g}{mol} }{0.082\frac{atm L}{molK} x498 K}[/tex]
and solving you get:
density= 3.06 g/L
Finally, the density of aluminum chloride vapor (AlCl₃) at 498 K and 0.939 atm is 3.06 g/L.
Learn more about
density:
brainly.com/question/952755
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ideal gas law:
https://brainly.com/question/4147359
