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"
