High School

How many grams are in [tex]$7.00 \times 10^{22}$[/tex] molecules of NaOH?

A. 46.5
B. 4.65
C. 7.0
D. 11.6
E. 6.65

Answer :

To find out how many grams are in [tex]\(7.00 \times 10^{22}\)[/tex] molecules of NaOH, we need to follow these steps:

1. Determine the Molar Mass of NaOH:
- Sodium (Na) has an atomic mass of approximately 23.00 g/mol.
- Oxygen (O) has an atomic mass of approximately 16.00 g/mol.
- Hydrogen (H) has an atomic mass of approximately 1.00 g/mol.
- Therefore, the molar mass of NaOH is [tex]\(23.00 + 16.00 + 1.00 = 40.00\)[/tex] g/mol.

2. Use Avogadro's Number:
- Avogadro's number, which is the number of molecules in one mole, is [tex]\(6.022 \times 10^{23}\)[/tex].

3. Calculate the Number of Moles of NaOH:
- To find the number of moles, we divide the given number of molecules by Avogadro's number:
[tex]\[
\text{Number of moles} = \frac{7.00 \times 10^{22}}{6.022 \times 10^{23}}
\][/tex]
- This calculation gives approximately 0.116 moles of NaOH.

4. Calculate the Mass in Grams:
- To find the mass in grams, multiply the number of moles by the molar mass of NaOH:
[tex]\[
\text{Mass in grams} = 0.116 \times 40.00 = 4.65 \text{ grams}
\][/tex]

Therefore, the correct answer is approximately 4.65 grams, which corresponds to option b: 4.65 grams.