Question #3ccd4

1 Answer
Oct 18, 2017

Answer:

#"1.6 g L"^(-1)#

Explanation:

Your tool of choice here is the ideal gas law equation, which looks like this

#color(blue)(ul(color(black)(PV = nRT)))#

Here

  • #P# is the pressure of the gas
  • #V# is the volume it occupies
  • #n# is the number of moles of gas present in the sample
  • #R# is the universal gas constant, equal to #0.0821("atm L")/("mol K")#
  • #T# is the absolute temperature of the gas

Now, the problem wants you to find the density of nitrogen dioxide in a volume of #"150 L"#, at a temperature of

#28^@"C" = 28^@"C" + 273.15 = "301.15 K"#

and a pressure of #"0.85 atm"#.

As you know, the density of a substance, #rho#, tells you the mass of exactly #1# unit of volume of said substance. This implies that you can calculate the density of a substance by dividing the mass of a given sample, let' say #m#, and the volume it occupies, #V#.

#color(blue)(rho = m/V)#

Now, notice that the ideal gas law equation uses the number of moles of gas, #n#. As you know, the number of moles of a substance can be expressed as a ratio between the mass of a given sample, #m#, and the molar mass of the substance, let's say #M_M#.

#n = m/M_M#

Plug this into the ideal gas law equation to get

#PV = m/M_M * RT#

All you have to do now is to rearrange this equation in order to find an expression for the density of the gas.

#P = color(blue)(m)/(M_M * color(blue)(V)) * RT#

#P * M_M = color(blue)(m)/color(blue)(V) * RT#

This means that you have

#P * M_M = color(blue)(rho) * RT#

which gets you

#color(blue)(rho) = (P * M_M)/(RT)#

Finally, plug in your values to find

#rho = (0.85 color(red)(cancel(color(black)("atm"))) * "46.0 g" color(red)(cancel(color(black)("mol"^(-1)))))/(0.0821(color(red)(cancel(color(black)("atm"))) * "L")/(color(red)(cancel(color(black)("mol"))) * color(red)(cancel(color(black)("K")))) * 301.15 color(red)(cancel(color(black)("K")))) = color(darkgreen)(ul(color(black)("1.6 g L"^(-1))))#

The answer is rounded to two sig figs.

Notice that you didn't need to know the volume of the gas in order to be able to find its density.