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

Question

Natalie Anton · Accepted Answer

#"7.4 atm"#

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

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

#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

#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#

#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.

Wyatt Adkins · Answer

undefined 5.92 atm.