# A 21-liter cylinder contains 1.5 moles of an ideal gas at 311 K. What is the pressure of the gas?

##### 1 Answer

#### Explanation:

This is a pretty straightforward ideal gas law equation practice problem.

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

#color(blue)(PV = nRT)" "# , where

*universal gas constant*, usually given as

**always** expressed in *Kelvin*

So, the problem provides you with

the,volumeof the gas#V = "21 L"# the,number of molesof gas#n = 1.5# the,absolute temperatureof the gas#T = "311 K"#

Since you know the value of

#PV = nRT implies P = (nRT)/V#

Next, make sure that the **units** given to you **match** those used in the expression of the universal gas constant.

# {:(color(red)("Need"), color(white)(aaaaa), color(blue)("Have")), (color(white)(aaaa), color(white)(aaaa), color(white)(aaaa)), (color(white)(aa)"L", color(white)(aaaa), color(white)(aa)"L"color(white)(aaaaaa)color(green)(sqrt())), ("moles", color(white)(aaaa), "moles"color(white)(aaaaa)color(green)(sqrt())), (color(white)(aa)"K", color(white)(aaaa), color(white)(aa)"K"color(white)(aaaaaa)color(green)(sqrt())) :}#

The units given to you match those used for

#P = (1.5 color(red)(cancel(color(black)("moles"))) * 0.0821("atm" * color(red)(cancel(color(black)("L"))))/(color(red)(cancel(color(black)("mol"))) * color(red)(cancel(color(black)("K")))) * 311color(red)(cancel(color(black)("K"))))/(21color(red)(cancel(color(black)("L"))))#

#P = "1.824 atm"#

Rounded to two sig figs, the number of sig figs you have for the volume and number of moles of gas, the answer will be

#P = color(green)("1.8 atm")#