Question

What is the atomic fraction of zinc in aluminum for a two-component alloy containing 10 wt.% zinc? atomic weight for zinc is 65.39 g/mol and that of aluminum is 26.9 g/mol. (a)?

Answer 1

Answer : The correct answer for atomic fraction of Zn is 4.37

Following are the steps to find atomic fraction of Zinc in Zn-Al alloy :

Step 1 : Find mass of Zn in alloy .

Given : wt%( weight % ) of Zn = 10%

Lets assume complete mass of alloy is 100g ,so the mass of Zn =>

`Wt percent = (mass of Zn)/(mass of alloy)`

`10 percent = (mass of Zn)/(100g)`

`(10)/(100) = (mass of Zn)/(100g)`

Multiplying both side by 100 g

`(10)/(100) * 100 g = (mass of Zn)/(100g) * 100g`

Mass of Zn = 10 g

Step 2: To find mass of Al.

Mass of alloy = (mass of Al + mass of Zn )

100 g = Mass of Al + 10 g

Mass of Al = 90 g

Step 3 : To find moles of both Al and Zn

`Mole = (mass )/(molar mass)`

Given : Mass of Zn = 10 g Molar mass of Zn = 65.39 g/mol

`Mole of Zn = (10 g )/(65.39(g)/(mol))`

Mole of Zn = 0.153 mol

Given : Mass of Al = 90 g Molar mass of Al = 26.9 g/mol

`Mole of Al = (90 g)/(26.9 (g)/(mol))`

Mole of Al = 3.346 mol

Step 4 : To find number of atoms of Zn and Al .

In 1 mole of any element , the number of atoms present is 6.022 x 10²³ atoms present .

Hence ,
`Number of atoms of Zn = 0.153 mol * (6.022 * 10^2^3)/(1 mol)`

Number of atoms of Zn = 0.921 * 10²³

And ,
`Number of atoms of Al = 3.346 mol * (6.022 * 10^2^3)/(1 mol)`

Number of atoms of Al = 20.150 * 10²³

Step 5 : Find atomic fraction of Zn ]

`Atomic fraction of an element = (number of atoms of element )/(Total number of atoms in alloy) *100`

Number of Atoms of Zn = 0.921 * 10²³

Total number of atoms = Atoms of Zn + Atoms of AL

= 0.921 * 10²³ + 20.150 * 10²³ = 21.071 * 10²³

Plugging these values in formula of atomic fraction =>

`Atomic fraction of Zn = (0.921 * 10^2^3)/(21.071 * 10^2^3) * 100`

= 0.0437 * 100

Atomic fraction of Zn = 4.37