A 283.3-g sample of #X_2(g)# has a volume of 30 L at 3.2 atm and 27°C. What is element #X#?
1 Answer
Chlorine,
Explanation:
Your strategy here is to apply the ideal gas law equation to find the number of moles of gas present in your sample.
In order to be able to identify the unknown element, you need to know its molar mass. A substance's molar mass tells you the mass of one mole of that substance.
The important thing to notice here is that you're given a sample of
Since you know the mass of your sample, you can use the number of moles it contains to determine the element's molar mass.
So, the ideal gas law equation looks like this
#color(blue)(PV = nRT)" "# , where
Rearrange the equation to solve for
#PV = nRT implies n = (PV)/(RT)#
Plug in your values - do not forget to convert the temperature of the gas from degrees Celsius, to Kelvin
#n = (3.2 color(red)(cancel(color(black)("atm"))) * 30color(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")))) = "3.896 moles"#
So, if
#1color(red)(cancel(color(black)("mole"))) * "283.3 g"/(3.896color(red)(cancel(color(black)("moles")))) = "72.7 g"#
Since one mole of
Now, a molecule of
#M_M = 1/2 * "72.7 g mol"^(-1) = "36.25 g mol"^(-1)#
The closest match to this value is the molar mass of chlorine,