# Question #f6a82

##### 1 Answer

Here's what I got.

#### Explanation:

The idea here is that STP conditions are *usually* given to you as a pressure of

#0^@"C" = 0^@"C" + 273.15 = "273.15 K"#

Under these specific conditions for pressure and temperature, **mole** of any ideal gas occupies **molar volume of a gas** at STP.

Now, room conditions are usually given to you as a pressure of

#20^@"C" + 273.15 = "293.15 K"#

our goal here is to figure out the volume occupied by **mole** of any ideal gas at room temperature. To do that, use the **ideal gas law equation**

#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

Rearrange the equation

#V/n = (RT)/P#

Plug in your values to get

#V/n = (0.0821 (color(red)(cancel(color(black)("atm"))) * "L")/("mol" * color(red)(cancel(color(black)("K")))) * 293.15 color(red)(cancel(color(black)("K"))))/(1 color(red)(cancel(color(black)("atm"))))#

#V/n = "24.07 L mol"^(-1)#

This means that **mole** of any ideal gas occupies

Now all you have to do is use the **molar mass** of nitrogen gas to determine how many *moles* you have in your sample

#35 color(red)(cancel(color(black)("g"))) * "1 mole n"_2/(28.0134color(red)(cancel(color(black)("g")))) = "1.249 moles N"_2#

and use the molar volume of a gas at room conditions to find the volume it occupies

#1.249 color(red)(cancel(color(black)("moles N"_2))) * "24.07 L"/(1color(red)(cancel(color(black)("mole N"_2)))) = color(darkgreen)(ul(color(black)("30. L")))#

The answer is rounded to two **sig figs**, the number of sig figs you have for the mass of nitrogen as.

**SIDE NOTE** *Plug in the values for pressure and temperature you have at STP into this equation*

#V/n = (RT)/P#

*You should end up with*

#V/n = "22.4256 mol L"^(-1) ~~ "22.4 mol L"^(-1)#

*This is why we can say that 1 mole of any ideal gas occupies*

*under STP conditions*.