# What pressure will be exerted by 2.01 mol hydrogen gas in a 6.5 L cylinder at 20°C?

##### 1 Answer

#### Explanation:

In order to be able to solve this problem, you must be familiar with 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

In your case, you must find the pressure exerted by the gas, so rearrange the ideal gas law equation to isolate

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

Now, before plugging in your values, make sure that the units given to you by the problem **match** those used in the expression of the universal gas constant.

In this case, you have

In this case, you have

#ul(color(white)(aaaacolor(black)("What you have")aaaaaaaaaacolor(black)("What you need")aaaaa))#

#color(white)(aaaaaacolor(black)("liters " ["L"])aaaaaaaaaaaaaaacolor(black)("liters " ["L"])aaaa)color(darkgreen)(sqrt())#

#color(white)(aaaaacolor(black)("moles " ["mol"])aaaaaaaaaaaaacolor(black)("moles " ["mol"])aaa)color(darkgreen)(sqrt())#

#color(white)(acolor(black)("degrees Celsius " [""^@"C"])aaaaaaaaaacolor(black)("Kelvin " ["K"])aaaa)color(red)(xx)#

To convert the temperature from degrees Celsius to Kelvin, use the conversion factor

#color(blue)(ul(color(black)(T["K"] = t[""^@"C"] + "273.15")))#

Plug in your values into the above equation and solve for

#P = (2.01 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")))) * (20 + 273.15) color(red)(cancel(color(black)("K"))))/(6.5 color(red)(cancel(color(black)("L"))))#

#color(darkgreen)(ul(color(black)(P = "7.4 atm")))#

I'll leave the answer rounded to two **sig figs**, but keep in mind that you only have one significant figure for the temperature of the gas.