Calculate the density of nitrogen gas at a temperature of 101 °c and at a pressure of 1.00 atm. express your answer in g/l.

The density is given by the following formula:

  (1)

Where is the mass and the volume.

On the other hand, the Ideal Gas equation is:

  (2)

Where:

is the pressure of the gas

the number of moles of gas

is the gas constant

is the absolute temperature of the gas in Kelvin.

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

Then:

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

  (3)

It is known the number of moles of gas is given by:

  (4)

Where is the mass of the gas and its molecular mass.

In the case of Nitrogen

Substituting (4) in (3) and simplifying:

  (5)

Dividing by in both sides:

  (6)

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

  (7)

  (8)

Remembering equation (1): we can substitute it in (8)

  (9)>>>>Now we can find the density of nitrogen gas with the known values

Finally:

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y