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Answer: 0.911 g/L

The density [tex]d[/tex] is given by the following formula:

[tex]d=\frac{m}{V}[/tex]   (1)

Where [tex]m[/tex] is the mass and [tex]V[/tex] the volume.

On the other hand, the Ideal Gas equation is:

[tex]P.V=n.R.T[/tex]   (2)

Where:

[tex]P[/tex] is the pressure of the gas

[tex]n[/tex] the number of moles of gas

[tex]R=0.0821\frac{L.atm}{mol.K}[/tex] is the gas constant

[tex]T[/tex] is the absolute temperature of the gas in Kelvin.

This means the  101 °C must be converted to Kelvin, using the following formula:

[tex]\ºC+273.15=K[/tex]

Then: [tex]101\ºC+273.15=374.15K[/tex]

Now, we are going to rewrite equation (2) to find the volume:

[tex]V=\frac{n.R.T}{P}[/tex]   (3)

It is known the number of moles of gas [tex]n[/tex] is given by:

[tex]n=\frac{m}{MM}[/tex]   (4)

Where [tex]m[/tex] is the mass of the gas and [tex]MM[/tex] its molecular mass.

In the case of Nitrogen [tex]MM=28.0134\frac{g}{mol}[/tex]

Substituting (4) in (3) and simplifying:

[tex]V=\frac{m.R.T}{MM.P}[/tex]   (5)

Dividing by [tex]m[/tex] in both sides:

[tex]\frac{V}{m}=\frac{R.T}{MM.P}[/tex]   (6)

The next step is to elevate both sides to the power of [tex]-1[/tex], in order to have the inverse of this expression and write it in terms of the density:

[tex](\frac{V}{m})^{-1} =(\frac{R.T}{MM.P})^{-1}[/tex]   (7)

[tex]\frac{m}{V}=\frac{MM.P}{R.T}[/tex]   (8)

Remembering equation (1): [tex]d=\frac{m}{V}[/tex] we can substitute it in (8)

[tex]d=\frac{MM.P}{R.T}[/tex]   (9)>>>>Now we can find the density of nitrogen gas with the known values

[tex]d=\frac{(28.0134\frac{g}{mol})(1atm)}{(0.0821\frac{L.atm}{mol.K})(374.15K)}[/tex]

Finally:

[tex]d=0.911\frac{g}{L}[/tex]

Lanuel

The density of nitrogen gas at a temperature of 101 °C is equal to [tex]0.911\;g/L[/tex]

Given the following data:

Temperature = 101°C = 273 + 100 = 373 K.

Pressure = 1.00 atm.

Scientific data:

Molar mass of nitrogen gas = 28.01 g/mol.

Ideal gas constant = 0.0821.

How to calculate the density.

Mathematically, the density of an ideal gas is given by this formula:

[tex]\rho = \frac{M_m P}{RT}[/tex]

Where:

  • P is the pressure.
  • R is the ideal gas constant.
  • T is the temperature.
  • [tex]M_m[/tex] is the molar mass.

Substituting the given parameters into the formula, we have;

[tex]\rho = \frac{28.01 \times 1 }{0.0821 \times 373}\\\\\rho =0.911\;g/L[/tex]

Read more on density here: brainly.com/question/3173452

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