The charge on 500 cc of water due to protons will be

Options

A. `6.1 xx 10^(27) C `
B. `2.67 xx 10^(-7) C `
C. `6 xx 10^(23) C`
D. `1.67 xx 10^(23) C`

Answer

To find the charge on 500 cc of water due to protons, we can follow these steps:

### Step 1: Convert volume of water to mass
Given that 500 cc of water is equivalent to 500 ml, we can convert this to mass using the density of water (1 g/cm³).

\[ \text{Mass of water} = 500 \, \text{g} \]

### Step 2: Calculate the number of moles of water
The molecular mass of water (H₂O) is approximately 18 g/mol. We can calculate the number of moles of water using the formula:

\[ \text{Number of moles} = \frac{\text{Mass of water}}{\text{Molecular mass of water}} = \frac{500 \, \text{g}}{18 \, \text{g/mol}} \approx 27.78 \, \text{moles} \]

### Step 3: Calculate the number of water molecules
Using Avogadro's number (approximately \(6.022 \times 10^{23}\) molecules/mol), we can find the total number of water molecules in 27.78 moles:

\[ \text{Total number of water molecules} = \text{Number of moles} \times \text{Avogadro's number} = 27.78 \times 6.022 \times 10^{23} \approx 1.67 \times 10^{25} \, \text{molecules} \]

### Step 4: Calculate the total number of protons
Each water molecule (H₂O) contains 10 protons (2 from hydrogen and 8 from oxygen). Therefore, the total number of protons can be calculated as:

\[ \text{Total number of protons} = \text{Total number of water molecules} \times 10 = 1.67 \times 10^{25} \times 10 = 1.67 \times 10^{26} \, \text{protons} \]

### Step 5: Calculate the total charge due to protons
The charge of a single proton is approximately \(1.6 \times 10^{-19}\) coulombs. Thus, the total charge due to protons is:

\[ \text{Total charge} = \text{Total number of protons} \times \text{Charge of a proton} = 1.67 \times 10^{26} \times 1.6 \times 10^{-19} \approx 2.67 \times 10^{7} \, \text{coulombs} \]

### Final Answer
The charge on 500 cc of water due to protons is approximately \(2.67 \times 10^{7} \, \text{coulombs}\).

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