Question

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

Answer 1

Solution:

$\text{mass of NaOH = 2.90 × 10²² NaOH formula units} × \frac{\text{1 mol NaOH}}{\text{6.022 × 10²³ NaOH formula units}} × \frac{\text{40.0 g NaOH}}{\text{1 mol NaOH}}$

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

Answer 2

Answer:

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

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.