Answer to Question #235462 in Chemistry for Dotun

Question

An alloy of Co, Rh and Mn contains these elements in the atomic ratio of 2 : 5 : 2 , respectively. What is the mass of a sample of this alloy containing a total of 8.75 x 1021 atoms ?

Answer 1

Solution:

N(Co) : N(Rh) : N(Mn) = 2 : 5 : 2

Co: 2x

Rh: 5x

Mn: 2x

2x + 5x + 2x = 8.75×10²¹ atoms

9x = 8.75×10²¹ atoms

x = 9.72×10²⁰ atoms

Hence,

N(Co) = 2x = 2 × 9.72×10²⁰ atoms = 1.95×10²¹ atoms

N(Rh) = 5x = 5 × 9.72×10²⁰ atoms = 4.86×10²¹ atoms

N(Mn) = 2x = 2 × 9.72×10²⁰ atoms = 1.95×10²¹ atoms

One mole of any substance contains 6.022×10²³ atoms/molecules.

Hence,

n(Co) = (1.95×10²¹ atoms) × (1 mol / 6.022×10²³ atoms) = 0.00324 mol

n(Rh) = (4.86×10²¹ atoms) × (1 mol / 6.022×10²³ atoms) = 0.00807 mol

n(Mn) = (1.95×10²¹ atoms) × (1 mol / 6.022×10²³ atoms) = 0.00324 mol

The molar mass of Co is 58.9332 g/mol

The molar mass of Rh is 102.9055 g/mol

The molar mass of Mn is 54.938 g/mol

Hence,

m(Co) = (0.00324 mol Co) × (58.9332 g Co / 1 mol Co) = 0.19094 g Co

m(Rh) = (0.00807 mol Rh) × (102.9055 g Rh / 1 mol Rh) = 0.83045 g Rh

m(Mn) = (0.00324 mol Mn) × (54.938 g Mn / 1 mol Mn) = 0.17799 g Mn

The mass of a sample = m(Co) + m(Rh) + m(Mn)

The mass of a sample = 0.19094 g + 0.83045 g + 0.17799 g = 1.19938 g = 1.2 g

The mass of a sample = 1.2 g

Answer: The mass of a sample of this alloy is 1.2 g