The elements A and Z combine to produce two different compounds: #A_2Z_3# and #AZ_2#. If 0.15 mole of #A_2Z_3# has a mass of 15.9 g and 0.15 mole of #AZ_2# has a mass of 9.3 g, what are the atomic masses of A and Z?
1 Answer
Explanation:
All you have to do here is set up a system of two equations with two unknowns, the molar mass of
Once you know the molar masses of the two elements, you can use a simple conversion factor to find their respective atomic masses.
So, you know that
#1 color(red)(cancel(color(black)("mole A"_2"Z"_3))) * "15.9 g"/(0.15color(red)(cancel(color(black)("moles A"_2"Z"_3)))) = "106 g"#
Notice that one mole of
- two moles of
#"A"# ,#2 xx "A"# - three moles of
#"Z"# ,#3 xx "Z"#
If you take
#2 * a + 3 * z = "106 g"" " " "color(orange)((1))#
Now do the same for
#1 color(red)(cancel(color(black)("mole AZ"_2))) * "9.3 g"/(0.15color(red)(cancel(color(black)("moles AZ"_2)))) = "62 g"#
This time, in one mole of
- one mole of
#"A"# ,#1 xx "A"# - two moles of
#"Z"# ,#2 xx "Z"#
You will thus have
#a + 2 * z = "62 g"" " " "color(orange)((2))#
Use equation
#a = 62 - 2z#
Plug this into equation
#2 * (62 - 2z) + 3 * z= 106#
#124 - 4z + 3z = 106#
Rearrange to find
#z = 18#
This means that you have
#a = 62 - 2 * 18 = 26#
So, you know that the molar masses of the two elements are
#"For A: " "26 g mol"^(-1)#
#"For B: " "18 g mol"^(-1)#
To convert these to atomic masses, use the conversion factor
#color(purple)(bar(ul(|color(white)(a/a)color(black)("1 u " = " 1 g mol"^(-1))color(white)(a/a)|)))#
You will have
#"For A: " m_"a A" = "26 u"#
#"For B: " m_"a Z" = "18 u"#
