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 =>

$Wt percent = \frac{mass of Zn}{mass of alloy}$

$10 percent = \frac{mass of Zn}{100g}$

$\frac{10}{100} = \frac{mass of Zn}{100g}$

Multiplying both side by 100 g

$\frac{10}{100} * 100 g = \frac{mass of Zn}{100g} * 100g$

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

$Mole = \frac{mass }{molar mass}$

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

$Mole of Zn = \frac{10 g }{65.39\frac{g}{mol}}$

Mole of Zn = 0.153 mol

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

$Mole of Al = \frac{90 g}{26.9 \frac{g}{mol}}$

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 , $Number of atoms of Zn = 0.153 mol * \frac{6.022 * 10^2^3}{1 mol}$

Number of atoms of Zn = 0.921 * 10²³

And , $Number of atoms of Al = 3.346 mol * \frac{6.022 * 10^2^3}{1 mol}$

Number of atoms of Al = 20.150 * 10²³

Step 5 : Find atomic fraction of Zn ]

$Atomic fraction of an element = \frac{number of atoms of element }{Total number of atoms in alloy} *100$

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 =>

$Atomic fraction of Zn = \frac{0.921 * 10^2^3}{21.071 * 10^2^3} * 100$

= 0.0437 * 100

Atomic fraction of Zn = 4.37