An unknown element #"X"# with oxygen forms a gas compound #"X"_2"O"# whose density at #-120^@"C"# and a pressure of #"320 mmHg"# is #"1.809 g/L"#. What is element #"X"#?
1 Answer
Here's what I got.
Explanation:
Your starting point here will be to use the ideal gas law equation and the density of this compound to find its molar mass.
#color(blue)(ul(color(black)(PV = nRT)))#
Here
#P# is the initial pressure of the gas#V# is the volume it occupies#n# is the number of moles of gas present in the mixture#R# is the universal gas constant, equal to#0.0821("atm L")/("mol K")# #T# is the absolute temperature of the gas
Now, you know that when kept at a temperature of
To make the calculations easier, let's assume that we have exactly
#PV = nRT implies n = (PV)/(RT)#
Plug in your values to find--do not forget to convert the temperature of the gas to Kelvin and its pressure to atmospheres!
#n = (320/760 color(red)(cancel(color(black)("atm"))) * 1 color(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 + (-120)) color(red)(cancel(color(black)("K"))))#
#n = "0.03349 moles"#
Now, this sample has a mass of
#M_ ("M X"_2"O") = "1.809 g"/"0.03349 moles" = "54.16 g mol"^(-1)#
Notice that the chemical formula of the compound suggests that every
#2# moles of element#"X"# ,#2 xx "X"# #1# mole of oxygen,#1 xx "O"#
Since elemental oxygen gas a molar mass of about
#"mass X" = "54.16 g " - " 16.0 g"#
#"mass X"# #=# #"38.16 g"#
This is the mass of exactly
#M_ ("M X") = "38.16 g"/"2 moles" = "19.08 g mol"^(-1)#
Rounded to two sig figs, the molar mass of element
#M_ ("M X") = "19 g mol"^(-1)#
The closest match that you have for the identity of element
#M_ ("M F") = "18.998 g mol"^(-1)#
This would make the unknown compound oxygen difluoride,