Question

How many MOLECULES are in 5.0 grams of sodium chloride? (Use "molecules" as your unit...Enter as 9.9 x 10^99 molecules)

Answer 1

`\boxed {\boxed {\sf 5.2 *10^(22) \ molecules \ NaCl}}`

Step-by-step explanation:

1. Convert grams to moles

First, convert grams to moles using the molar mass. This can be found on the Periodic Table.

• Na: 22.9897693 g/mol
• Cl: 35.45 g/mol

Sodium (Na) has an oxidation state of +1 and chlorine (Cl) has an oxidation state of -1, so they combine in a 1:1 ratio for a formula of NaCl. We can simply add their moles masses.

• NaCl: 22.9897693 g/mol + 35.45 g/mol = 58.4397693 g/mol

Use this as a ratio.

`\frac {58.4397693 \ g \ NaCl}{ 1 \ mol \ NaCl}`

Multiply by the given number of grams.

`5.0 \ g \ NaCl *\frac {58.4397693 \ g \ NaCl}{ 1 \ mol \ NaCl}`

Flip the fraction so the grams of sodium chloride cancel.

`5.0 \ g \ NaCl *\frac {1 \ mol \ NaCl}{ 58.4397693 \ g \ NaCl}`

`5.0 *\frac {1 \ mol \ NaCl}{ 58.4397693 }=\frac {5.0 \ mol \ NaCl} { 58.4397693 } = 0.0855581749 \ mol \ NaCl`

2. Convert moles to molecules

We must use Avogadro's Number. This tells us the amount of particles (molecules, atoms, etc.) in 1 mole of a substance. In this case, it is molecules of sodium chloride.

`\frac{6.022*10^(23) \ molecules \ NaCl} {1 \ mol \ NaCl}`

Multiply by the number of moles we calculated.

`0.0855581749 \ mol \ NaCl*\frac{6.022*10^(23) \ molecules \ NaCl} {1 \ mol \ NaCl}`

The moles of sodium chloride cancel.

`0.0855581749 *(6.022*10^(23) \ molecules \ NaCl)/(1)=5.15231329*10^(22) \ molecules \ NaCl`

The original measurement of grams has 2 (2 and 0) significant figures, so our answer must have the same. For the number we calculated, that is the hundredth place. The 5 in the hundredth place tells us to round the 1 to a 2.

`5.2 *10^(22) \ molecules \ NaCl`