8g of #"E"_2"O"_3# contain 5.6g of #"E"#. How many moles of #"E"# does a 16.8-g smaple of element #"E"# contain?

1 Answer
Nov 15, 2016

Answer:

#"0.3 moles"#

Explanation:

The first thing to notice here is that #1# mole of your unknown compound contains

  • two moles of element #"E"#, #2 xx "E"#
  • three moles of oxygen, #3 xx "O"#

Now, use the total mass of the sample and the mass of element #"E"# to calculate the mass of oxygen.

#color(blue)(ul(color(black)("mass of sample" = "mass of E" + "mass of O")))#

Plug in your values to find

#"mass of O" = "8 g" - "5.6 g" = "2.4 g"#

Use the molar mass of oxygen to calculate how many moles you have in this sample of #"E"_2"O"_3#

#2.4 color(red)(cancel(color(black)("g"))) * "1 mole O"/(16.0color(red)(cancel(color(black)("g")))) = "0.15 moles O"#

This means that the #"8-g"# sample of #"E"_2"O"_3# contains

#0.15 color(red)(cancel(color(black)("moles O"))) * "2 moles E"/(3color(red)(cancel(color(black)("moles O")))) = "0.10 moles E"#

Now, notice that you have

#(16.8 color(red)(cancel(color(black)("g E"))))/(5.6 color(red)(cancel(color(black)("g E")))) = 3#

This means that #"16.8 g"# of element #"E"# will contain three times as many moles as #"5.6 g"# of element #"E"#.

Therefore, you can say that

#color(darkgreen)(ul(color(black)("moles E in 16.8 g" = 3 xx "0.10 moles" = "0.3 moles")))#

The answer must be rounded to one significant figure.