Question

What is the mass of 2.90 ×1022 formula units of NaOH (Molar mass = 40.0 g/mol)?

Answer 1

`\boxed{\text{mass of NaOH = 1.926 g}}`

Answer 2

`\boxed {\boxed {\sf 1.93 \ g \ NaOH}}`

Step-by-step explanation:

1. Convert Formula Units to Moles

To do this, we use Avogadro's Number: 6.02*10²³. It is the number of particles (atoms, molecules, formula units, etc.) in 1 mole of a substance. In this case, it is formula units of sodium hydroxide.

`\frac {6.02*10^(23) \ formula \ units \ NaOH}{1 \ mol \ NaOH}`

Multiply by the given number of formula units.

`2.90*10^(22) \ formula \ units \ NaOH*\frac {6.02*10^(23) \ formula \ units \ NaOH}{1 \ mol \ NaOH}`

Flip the ratio so the formula units will cancel.

`2.90*10^(22) \ formula \ units \ NaOH*\frac {1 \ mol \ NaOH}{6.02*10^(23) \ formula \ units \ NaOH}`

`2.90*10^(22)*\frac {1 \ mol \ NaOH}{6.02*10^(23)}`

`\frac {2.90*10^(22) \ mol \ NaOH}{6.02*10^(23)}=0.04817275748 \ mol \ NaOH`

2. Convert Moles to Grams

For this, we use the molar mass. It is the grams per mole of a substance. We are given this value for sodium hydroxide: 40.0 g/mol

`\frac {40.0 \ g\ NaOH}{1 \ mol \ NaOH}`

Multiply by the moles we calculated.

`0.04817275748 \ mol \ NaOH*\frac {40.0 \ g\ NaOH}{1 \ mol \ NaOH}`

The moles cancel.

`0.04817275748 *\frac {40.0 \ g\ NaOH}{1 }`

`0.04817275748 *{40.0 \ g\ NaOH=1.926910299 \ g\ NaOH`

3. Round

The original measurement of formula units has 3 significant figures, so our answer must have the same. For the number we calculated that is the hundredth place.

`1.92\underline6 910299 \ g \ NaOH`

The 6 in the thousandth place tells us to round the 2 to a 3.

`1.93 \ g \ NaOH`

There are approximately 1.93 grams of sodium hydroxide.