Question

How many moles are there in 2.3 x 1024 atoms of
sulfur?

Answer 1

Step-by-step explanation:

The steps given in the question are incorrect.

Step 1 should be convert atoms to moles (n). Step 2 should be convert moles (n) to mass (m).

Step 1

Use dimensional analysis to convert the number of atoms to moles.

1 mole atoms = 6.022 × 10²³ atoms

n(Ag) = 2.3 × 10²⁴ Ag atoms × (1 mol Ag/6.022 × 10²³ Ag atoms) = 3.8193 mol Ag

Step 2

Convert the moles of Ag to mass.

mass (m) = moles (n) × molar mass (M)

n(Ag) = 3.8193 mol Ag

M(Ag) = atomic weight on the periodic table in g/mol = 107.868 g Ag/mol Ag

m(Ag) = 3.8193 mol × 107.868 g/mol = 412 g Ag = 410 g Ag rounded to two significant figures

The mass of 2.3 × 10²⁴ Ag atoms is approximately 410 g.

Answer 2

`\boxed {\boxed {\sf 3.8 \ moles \ of \ sulfur}}`

Step-by-step explanation:

We are asked to convert a number of atoms to moles.

We can convert atoms to moles using Avogadro's Number, which is 6.022 × 10²³. This is the number of particles (atoms, molecules, formula units, etc.) in 1 mole of a substance. In this problem, the particles are atoms of sulfur. There are 6.022 ×10²³ atoms of sulfur in 1 mole of sulfur.

We use dimensional analysis to convert atoms to moles. This involves setting up ratios. Use Avogadro's Number and the underlined information to make a ratio.

`\frac {6.022 * 10^(23) \ atoms \ S}{1 \ mol \ S}`

We are converting 2.3 ×10²⁴ atoms of sulfur to moles, so we multiply by this value.

`2.3 * 10^(24) \ atoms \ S *\frac {6.022 * 10^(23) \ atoms \ S}{1 \ mol \ S}`

Flip the ratio. It is equivalent, but it allows the units of atoms of sulfur to cancel.

`2.3 * 10^(24) \ atoms \ S *\frac {1 \ mol \ S}{6.022 * 10^(23) \ atoms \ S}`

`2.3 * 10^(24) *\frac {1 \ mol \ S}{6.022 * 10^(23) }`

`\frac {2.3 * 10^(24) }{6.022 * 10^(23) } \ mol \ S`

`3.819329127 \ mol \ S`

The original measurement of atoms (2.3 ×10²⁴) has 2 significant figures, so our answer must have the same. For the number we calculated that is the tenths place. The 1 in the hundredths place to the right (3.819329127) tells us to leave the 8 in the tenths place (3.819329127).

`3.8 \ mol \ S`

2.3 ×10²⁴ atoms of sulfur is equal to approximately 3.8 moles of sulfur.