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?

Question

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?

Peyton Adams · Accepted Answer

#m_"a A" = "26 u"#

#m_"a Z" = "18 u"# All you have to do here is set up a system of two equations with two unknowns, the molar mass of #"A"# and the molar mass of #"Z"#. 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 #0.15# moles of #"A"_2"Z"_3# have a mass of #"15.9 g"#. To make the calculations easier, calculate the mass of one mole of #"A"_2"Z"_3# #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 #"A"_2"Z"_3# contains If you take #a# to be the molar mass of #"A"# and #z# to be the molar mass of #"Z"#, you can say that #2 * a + 3 * z = "106 g"" " " "color(orange)((1))# Now do the same for #"AZ"_2#. You have #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 #"AZ"_2# you have You will thus have #a + 2 * z = "62 g"" " " "color(orange)((2))# Use equation #color(orange)((2))# to write #a = 62 - 2z# Plug this into equation #color(orange)((1))# to get #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"#

Natalie Anton · Answer

undefined The atomic mass of A is 7.0 g/mol, and the atomic mass of Z is 6.0 g/mol.