# Question #3ccd4

##### 1 Answer

#### Answer:

#### 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 theuniversal gas constant, equal to#0.0821("atm L")/("mol K")# #T# is theabsolute temperatureof the gas

Now, the problem wants you to find the **density** of nitrogen dioxide in a volume of

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

and a pressure of

As you know, the **density** of a substance, **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 **volume** it occupies,

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

Now, notice that the ideal gas law equation uses the number of *moles* of gas, **mass** of a given sample, **molar mass** of the substance, let's say

#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.