# Question #1a4dd

##### 1 Answer

#### Explanation:

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

So, 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

As you know, the **number of moles** present in a sample of gas, **mass** of that sample, **molar mass** of the gas,

#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#

Since you're interested in find the molar mass of the gas, rearrange to isolate

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

Notice that this equation contains a term that expresses the **mass** of the sample **per unit of volume**, i.e. the *density*,

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

This means that you have

#M_M = rho * (RT)/P#

Before plugging in your values, make sure that you convert the units for pressure and temperature to the units used in the expression of the ideal gas constant.

You will thus need to convert the pressure from *mmHg* to *atm* and the temperature from *degrees Celsius* to *Kelvin* by using

#color(purple)(|bar(ul(color(white)(a/a)color(black)("1 atm " = " 760 mmHg")color(white)(a/a)|)))" "# and#" " color(purple)(|bar(ul(color(white)(a/a)color(black)(T["K"] = t[""^@"C"] + 273.15)color(white)(a/a)|)))#

Also, notice that the density of the gas is expressed in *grams per cubic decimeter*, *grams per liter*,

#color(purple)(|bar(ul(color(white)(a/a)color(black)("1 L" = "1 dm"^3)color(white)(a/a)|)))" "#

The molar mass of the gas will be equal to

#M_M = 1.43 "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 + 27)color(red)(cancel(color(black)("K"))))/(608/760color(red)(cancel(color(black)("atm"))))#

#M_M =color(green)(|bar(ul(color(white)(a/a)"44 g mol"^(-1)color(white)(a/a)|)))#