Respuesta :
Solution:
[tex]\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}}[/tex]
[tex]\boxed{\text{mass of NaOH = 1.926 g}}[/tex]
Answer:
[tex]\boxed {\boxed {\sf 1.93 \ g \ NaOH}}[/tex]
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.
[tex]\frac {6.02*10^{23} \ formula \ units \ NaOH}{1 \ mol \ NaOH}[/tex]
Multiply by the given number of formula units.
[tex]2.90*10^{22} \ formula \ units \ NaOH*\frac {6.02*10^{23} \ formula \ units \ NaOH}{1 \ mol \ NaOH}[/tex]
Flip the ratio so the formula units will cancel.
[tex]2.90*10^{22} \ formula \ units \ NaOH*\frac {1 \ mol \ NaOH}{6.02*10^{23} \ formula \ units \ NaOH}[/tex]
[tex]2.90*10^{22}*\frac {1 \ mol \ NaOH}{6.02*10^{23}}[/tex]
[tex]\frac {2.90*10^{22} \ mol \ NaOH}{6.02*10^{23}}=0.04817275748 \ mol \ NaOH[/tex]
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
[tex]\frac {40.0 \ g\ NaOH}{1 \ mol \ NaOH}[/tex]
Multiply by the moles we calculated.
[tex]0.04817275748 \ mol \ NaOH*\frac {40.0 \ g\ NaOH}{1 \ mol \ NaOH}[/tex]
The moles cancel.
[tex]0.04817275748 *\frac {40.0 \ g\ NaOH}{1 }[/tex]
[tex]0.04817275748 *{40.0 \ g\ NaOH=1.926910299 \ g\ NaOH[/tex]
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.
[tex]1.92\underline6 910299 \ g \ NaOH[/tex]
The 6 in the thousandth place tells us to round the 2 to a 3.
[tex]1.93 \ g \ NaOH[/tex]
There are approximately 1.93 grams of sodium hydroxide.
