Answer:
To determine the number of grams in \( 7.5 \times 10^{26} \) molecules of NaCl, we need to follow these steps:
1. **Calculate the number of moles** of NaCl from the given number of molecules using Avogadro's number.
2. **Convert moles** of NaCl to grams using the molar mass of NaCl.
### Step 1: Calculate the number of moles
Avogadro's number (\( N_A \)) is approximately \( 6.022 \times 10^{23} \) molecules per mole. The number of moles (\( n \)) can be calculated as follows:
\[ n = \frac{\text{number of molecules}}{N_A} \]
Given:
- Number of molecules = \( 7.5 \times 10^{26} \)
- Avogadro's number = \( 6.022 \times 10^{23} \)
\[ n = \frac{7.5 \times 10^{26}}{6.022 \times 10^{23}} \]
Let's calculate \( n \):
\[ n \approx \frac{7.5 \times 10^{26}}{6.022 \times 10^{23}} \approx 1245.85 \, \text{moles} \]
### Step 2: Convert moles to grams
The molar mass of NaCl (sodium chloride) is the sum of the atomic masses of sodium (Na) and chlorine (Cl):
- Atomic mass of Na ≈ 23 g/mol
- Atomic mass of Cl ≈ 35.5 g/mol
- Molar mass of NaCl ≈ 23 + 35.5 = 58.5 g/mol
Now, we convert the moles to grams:
\[ \text{mass} = n \times \text{molar mass} \]
\[ \text{mass} = 1245.85 \, \text{moles} \times 58.5 \, \text{g/mol} \]
\[ \text{mass} \approx 72808.325 \, \text{grams} \]
So, \( 7.5 \times 10^{26} \) molecules of NaCl correspond to approximately 72808.33 grams.
