Question

A small cube of iron is observed under a microscope. The edge of the cube is 5.00×10 cm long. Find (a) the mass of the cube and (b) the number of iron atoms in the cube The molar mass of iron is 55.9g/mol, and its density is 7.86g/cm³.

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Answer 1

The mass of the cube is 9.82 kg and the number of iron atoms in the cube is 1.057×10^25 atoms.

Step-by-step explanation:

(a) To find the mass of the cube, we can use the formula:

mass = density x volume

Given that the edge of the cube is 5.00×10 cm, the volume of the cube can be calculated as:

volume = (edge length)^3 = (5.00×10 cm)^3 = 1.25×10^3 cm^3

Substituting the values into the formula, we have:

mass = 7.86 g/cm³ x 1.25×10^3 cm³ = 9.825×10^3 g = 9.82 kg

Therefore, the mass of the cube is 9.82 kg.

(b) To find the number of iron atoms in the cube, we can use Avogadro's number (6.02×10^23 atoms/mol).

First, we need to convert the mass of the cube into moles:

moles = mass / molar mass = 9.82 kg / 55.9 g/mol = 17.58 mol

Then, we can calculate the number of iron atoms:

number of atoms = moles x Avogadro's number = 17.58 mol x 6.02×10^23 atoms/mol = 1.057×10^25 atoms

Therefore, the number of iron atoms in the cube is 1.057×10^25 atoms.

Answer 2

Step-by-step explanation:

a) The mass of the cube can be calculated using the equation Mass = Volume x Density. The volume of the cube can be calculated as (5.00×10 cm)^3 = 125 cm³. Substituting this volume into the equation gives Mass = 125 cm³ x 7.86 g/cm³ = 983.5 g.

b) The number of iron atoms in the cube can be calculated using Avogadro's number (6.02 x 10^23 atoms/mol). The number of moles can be calculated using the molar mass of iron, 55.9 g/mol. Thus, the number of moles can be calculated as 983.5 g / 55.9 g/mol = 17.61 moles. Multiplying this by Avogadro's number gives the number of iron atoms in the cube as 1.07 x 10^24 atoms.