Question

Determine the composition of each of the following cobalt alloys.

a)One-third of the Co atoms are replaced by Zn atoms.

b) One-eighth of the Co atoms are replaced by Ti atoms.

c)One-third of the Co atoms are replaced by Zn atoms and one-sixth of the Co atoms are replaced by Ti atoms.

percent by mass of each

Answer 1

a)
mol of Co = 2/3 mol
mol of Zn = 1/3
Molar mass of Co= 28 g/mol
Molar mass of Zn = 65.4 g/mol

mass of Zn = number of moles of Zn * molar mass of Zn
                        = 1/3 * 65.4
                        = 21.8 g

mass of Co = number of moles of Co * molar mass of Co
                        = 2/3 * 28
                        = 18.7 g
Total mass = 21.8 + 18.7 = 40.5 g

% of Zn = mass of Zn * 100 / total mass
                = 21.8*100/40.5
                = 53.8 %

% Of Co = 100 - 53.8 =46.2 %

b)
mol of Co = 1-1/8 = 7/8 mol
mol of Ti = 1/8
Molar mass of Co= 28 g/mol
Molar mass of Ti = 47.9 g/mol

mass of Ti = number of moles of Ti * molar mass of Ti
                        = 1/8 * 47.9
                        = 6 g

mass of Co = number of moles of Co * molar mass of Co
                        = 7/8 * 28
                        = 24.5 g
Total mass = 6 + 24.5 = 30.5 g

% of Ti = mass of Ti * 100 / total mass
                = 6*100/30.5
                = 19.7 %

% Of Co = 100 - 19.7 =80.3 %

c)
mol of Zn = 1/3
mol of Ti = 1/6
mol of Co = 1-1/3 - 1/6 = 1/2
Molar mass of Co= 28 g/mol
Molar mass of Zn = 65.4 g/mol
Molar mass of Ti = 47.9 g/mol

mass of Ti = number of moles of Ti * molar mass of Ti
                        = 1/6 * 47.9
                        = 7.98 g

mass of Zn = number of moles of Zn * molar mass of Zn
                        = 1/3 * 65.4
                        = 21.8 g

mass of Co = number of moles of Co * molar mass of Co
                        = 1/2 * 28
                        = 14 g

Total mass = 7.98 + 21.8 + 14 = 43.78 g

% of Zn = mass of Zn * 100 / total mass
                = 21.8*100/43.78
                = 49.8 %

% of Ti = mass of Ti * 100 / total mass
                = 7.98*100/43.78
                = 18.2 %

% Of Co = 100 - 49.8 -18.2 = 32 %