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How many grams are in [tex]\( 9.28 \times 10^{23} \)[/tex] molecules of NaCl?

Choose the correct setup:

A. [tex]\( \frac{9.28 \times 10^{23} \text{ molecules}}{6.02 \times 10^{23} \text{ molecules}} \times 58.44 \text{ g} \)[/tex]

B. [tex]\( \frac{9.28 \times 10^{23} \text{ molecules}}{6.02 \times 10^{23} \text{ molecules}} \)[/tex]

C. [tex]\( \frac{9.28 \times 10^{23} \text{ molecules}}{1 \text{ mole}} \times 6.02 \times 10^{23} \text{ molecules} \)[/tex]

D. [tex]\( \frac{9.28 \times 10^{23} \text{ molecules}}{6.02 \times 10^{23} \text{ molecules}} \times 1 \text{ mole} \)[/tex]


Sagot :

To determine how many grams are in [tex]\( 9.28 \times 10^{23} \)[/tex] molecules of NaCl, we need to follow a series of steps. Here’s the detailed, step-by-step solution:

1. Understand the Given Data and Constants:
- Number of NaCl molecules ([tex]\( N \)[/tex]) = [tex]\( 9.28 \times 10^{23} \)[/tex]
- Molar mass of NaCl ([tex]\( M \)[/tex]) = 58.44 grams per mole
- Avogadro's number ([tex]\( N_A \)[/tex]) = [tex]\( 6.02 \times 10^{23} \)[/tex] molecules per mole

2. Convert Molecules to Moles:
First, we need to convert the given number of molecules to moles. One mole of any substance contains Avogadro's number of molecules.
[tex]\[ \text{Moles of NaCl} = \frac{\text{Number of molecules}}{\text{Avogadro's number}} \][/tex]
Substituting the given values:
[tex]\[ \text{Moles of NaCl} = \frac{9.28 \times 10^{23} \text{ molecules}}{6.02 \times 10^{23} \text{ molecules per mole}} \][/tex]

This simplifies approximately to:
[tex]\[ \text{Moles of NaCl} \approx 1.5415282392026577 \text{ moles} \][/tex]

3. Convert Moles to Grams:
Now that we know the number of moles, we convert moles to grams using the molar mass of NaCl.
[tex]\[ \text{Mass (in grams)} = \text{Moles} \times \text{Molar Mass} \][/tex]
Substituting in the known values:
[tex]\[ \text{Mass (in grams)} = 1.5415282392026577 \text{ moles} \times 58.44 \text{ grams per mole} \][/tex]

This gives a result of:
[tex]\[ \text{Mass (in grams)} \approx 90.0869102990033 \text{ grams} \][/tex]

Therefore, there are approximately 90.09 grams in [tex]\( 9.28 \times 10^{23} \)[/tex] molecules of NaCl.
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