Question

27. What is the mass of 2.34 x 1023 atoms of Sulfur?

a) 12.5 g
b) 1.25 x 1049
g
c) 1.25 x 1047 g

Answer 1

`\boxed {\boxed {\sf A. \ 12.5 \ grams}}`

Step-by-step explanation:

We are asked to find the mass of 2.34 × 10²³ atoms of sulfur (S)

1. Convert Atoms to Moles

First, we convert atoms to moles using Avogadro's Number of 6.022 × 10²³. This is the number of particles (atoms, molecules, formula units, etc.) in 1 mole of a substance. For this question, the particles are atoms of sulfur. There are 6.022 × 10²³ atoms of sulfur in 1 mole of sulfur.

We will convert using dimensional analysis, so we must set up a ratio.

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

We are converting 2.34 × 10²³ atoms of sulfur to moles, so we multiply the ratio by this value.

`2.34 * 10^(23) \ atoms \ S* \frac {6.022 * 10^(23) \ atoms \ S}{1 \ mol \ S}`

Flip the ratio so the units of atoms of sulfur cancel.

`2.34 * 10^(23) \ atoms \ S* \frac{1 \ mol \ S} {6.022 * 10^(23) \ atoms \ S}`

`2.34 * 10^(23)* \frac{1 \ mol \ S} {6.022 * 10^(23)}`

`\frac{2.34 * 10^(23)} {6.022 * 10^(23)} \ mol \ S`

`0.3885752242 \ mol \ S`

2. Convert Moles to Grams

Next, we convert moles to grams using the molar mass. This is the mass of 1 mole of a substance. The value is found on the Periodic Table as the atomic mass, but the units are grams per mole instead of atomic mass units. Look up sulfur's molar mass.

• S: 32.07 g/mol

Set up another ratio.

`\frac {32.07 \ g \ S}{ 1\ mol \ S}`

Multiply by the number of moles we calculated.

`0.3885752242 \ mol \ S *\frac {32.07 \ g \ S}{ 1\ mol \ S}`

The units of moles of sulfur cancel.

`0.3885752242 *\frac {32.07 \ g \ S}{ 1}`

`0.3885752242 * {32.07 \ g \ S}`

`12.46160744 \ g \ S`

3. Round

The original value of atoms (2.34 × 10²³) has 3 significant figures (2,3, 4), so our answer must have the same. For the number we calculated, that is the tenths place. The 6 in the hundredth place tells us to round the 4 up to a 5.

`12.5 \ g \ S`

There are 12.5 grams of sulfur in 2.34 × 10²³ atoms of sulfur.