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What is the density, in g/L, of methanol vapor at 400 K and 1.15 atm. The molar mass of methanol is 32.0 g/mol.

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CintiaSalazar

Taking into account the ideal gas law,  the density of methanol vapor is 1.1219 [tex]\frac{g}{L}[/tex].

Ideal gas law

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:

P×V = n×R×T

where

  • P is the gas pressure.
  • V is the volume that occupies.
  • T is its temperature.
  • R is the ideal gas constant. The universal constant of ideal gases R has the same value for all gaseous substances.
  • n is the number of moles of the gas.

Density of methanol

Now, taking into account this law, you get:

[tex]\frac{n}{V} =\frac{P}{RXT}[/tex]

The units are moles/L. So, in order to calculate the density, it is necessary to take into account the molar mass, in order to calculate the density as follows:

[tex]density =\frac{P}{RXT}xmolar mass[/tex]

Then, in this case, you know:

  • P= 1.15 atm
  • T= 400 K
  • R= 0.082 [tex]\frac{atmL}{molK}[/tex]
  • molar mass= 32[tex]\frac{g}{mol}[/tex]

Replacing in the previous expression:

[tex]density =\frac{1.15 atm}{0.082\frac{atmL}{molK} X400 K}x32 \frac{g}{mol}[/tex]

Solving:

density= 1.1219 [tex]\frac{g}{L}[/tex]

Finally, the density of methanol vapor is 1.1219 [tex]\frac{g}{L}[/tex].

Learn more about ideal gas law:

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