A solution contains 58.5 g of common salt in 360 g of water. Calculate the total number of protons in solution.

Options

A. `21 xx 6.023 xx 10^(23)`
B. `22.8 xx 6.023 xx 10^(23)`
C. `200 xx 6.023 xx 10^(23)`
D. `228 xx 6.023 xx 10^(23)`

Explanation

To solve the problem of calculating the total number of protons in a solution containing 58.5 g of common salt (NaCl) in 360 g of water (H₂O), we can follow these steps:

### Step 1: Determine the number of protons in NaCl
- The formula for common salt is NaCl.
- Sodium (Na) has 11 protons.
- Chlorine (Cl) has 17 protons.
- Therefore, the total number of protons in one molecule of NaCl = 11 (from Na) + 17 (from Cl) = **28 protons**.

### Step 2: Calculate the moles of NaCl
- The molar mass of NaCl = mass of Na + mass of Cl = 23 g/mol (Na) + 35.5 g/mol (Cl) = **58.5 g/mol**.
- To find the number of moles of NaCl in 58.5 g:
\[ \text{Moles of NaCl} = \frac{\text{mass}}{\text{molar mass}} = \frac{58.5 \, \text{g}}{58.5 \, \text{g/mol}} = **1 mole**. \]

### Step 3: Calculate the total number of protons from NaCl
- Since there is 1 mole of NaCl, the total number of molecules of NaCl is equal to Avogadro's number, \(6.022 \times 10^{23}\) molecules.
- Total protons from NaCl = Number of molecules × Protons per molecule:
\[ \text{Total protons from NaCl} = 1 \, \text{mole} \times 28 \, \text{protons/molecule} = 28 \, \text{moles of protons}. \]

### Step 4: Determine the number of protons in water (H₂O)
- The formula for water is H₂O.
- Each hydrogen (H) has 1 proton, and there are 2 hydrogen atoms, so:
- Protons from hydrogen = 2 × 1 = **2 protons**.
- Oxygen (O) has 8 protons.
- Therefore, the total number of protons in one molecule of H₂O = 2 (from H) + 8 (from O) = **10 protons**.

### Step 5: Calculate the moles of water
- The molar mass of water (H₂O) = 2 × 1 g/mol (H) + 16 g/mol (O) = **18 g/mol**.
- To find the number of moles of water in 360 g:
\[ \text{Moles of H₂O} = \frac{360 \, \text{g}}{18 \, \text{g/mol}} = 20 \, \text{moles}. \]

### Step 6: Calculate the total number of protons from water
- Total protons from water = Number of moles × Protons per molecule:
\[ \text{Total protons from H₂O} = 20 \, \text{moles} \times 10 \, \text{protons/molecule} = 200 \, \text{protons}. \]

### Step 7: Calculate the total number of protons in the solution
- Total protons in the solution = Total protons from NaCl + Total protons from H₂O:
\[ \text{Total protons} = 28 + 200 = 228 \, \text{protons}. \]

### Final Answer:
The total number of protons in the solution is **228 protons**.

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