Question

Question #3ccd4

Answer 1

`"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.