# Question #66004

##### 1 Answer

#### Explanation:

The idea here is that you need to use the **ideal gas law** equation to find a relationship between the density of the gas and its **molar mass**.

As you know, the ideal gas law equation looks like this

#color(blue)(|bar(ul(color(white)(a/a)PV = nRTcolor(white)(a/a)|)))" "# , where

*universal gas constant*, usually given as

**absolute temperature** of the gas

Now, the number of moles can be expressed using the *mass*, **molar mass**,

#color(purple)(|bar(ul(color(white)(a/a)color(black)(n = m/M_M)color(white)(a/a)|)))#

Plug this into the ideal gas law equation to get

#PV = m/M_M * RT" " " "color(red)("(*)")#

**Density** is defined as *mass* per unit of volume. If you take

#color(purple)(|bar(ul(color(white)(a/a)color(black)(rho = m/V)color(white)(a/a)|)))#

Notice that you can rearrange equation

#PV * M_M = m/color(red)(cancel(color(black)(M_M))) * RT * color(red)(cancel(color(black)(M_M)))#

Now divide both sides by

#(P * color(red)(cancel(color(black)(V))) * M_M)/color(red)(cancel(color(black)(V))) = m/V * RT#

Finally, isolate

#color(purple)(|bar(ul(color(white)(a/a)color(black)(M_M = rho * (RT)/P)color(white)(a/a)|)))#

Now, **STP** conditions are defined as a pressure of *kPa* to *atm* by using the conversion factor

#"1 atm " = " 101.325 kPa"#

Plug in your values to get

#M_M = 1.5"g"/color(red)(cancel(color(black)("L"))) * (0.0821(color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/("mol" * color(red)(cancel(color(black)("K")))) * (273.15 + 0)color(red)(cancel(color(black)("K"))))/(100/101.325color(red)(cancel(color(black)("atm"))))#

#M_M = color(green)(|bar(ul(color(white)(a/a)"34 g mol"^(-1)color(white)(a/a)|))) -># rounded to two sig figs

**SIDE NOTE** *Many sources still use STP conditions as a pressure of * #"1 atm"# *and a temperature of*

*If this is the definition of STP given to you, simply redo the calculations using these values for pressure and temperature. In this particular case, the answer will be the same because it must be rounded to two sig figs.*