Number of moles of water in 1 L of water with density 1 g/cc are

Options

A. 55.56
B. 45.56
C. 56.55
D. 5.655

Answer

To find the number of moles of water in 1 liter of water with a density of 1 g/cm³, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between density, mass, and volume**:
The formula for density (ρ) is given by:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
Rearranging this formula allows us to find mass:
\[ \text{Mass} = \text{Density} \times \text{Volume} \]

2. **Convert the volume from liters to cubic centimeters**:
Since 1 liter is equivalent to 1000 milliliters and 1 milliliter is equivalent to 1 cubic centimeter (cm³), we have:
\[ 1 \text{ L} = 1000 \text{ cm}^3 \]

3. **Substitute the values into the mass formula**:
Given that the density of water is 1 g/cm³, we can substitute the values:
\[ \text{Mass} = 1 \text{ g/cm}^3 \times 1000 \text{ cm}^3 = 1000 \text{ g} \]

4. **Use the molar mass of water to find the number of moles**:
The molar mass of water (H₂O) is approximately 18 g/mol. We can use the formula for the number of moles (n):
\[ n = \frac{\text{Mass}}{\text{Molar Mass}} \]
Substituting the values we have:
\[ n = \frac{1000 \text{ g}}{18 \text{ g/mol}} \approx 55.56 \text{ moles} \]

5. **Conclusion**:
The number of moles of water in 1 liter of water with a density of 1 g/cm³ is approximately 55.56 moles.

### Final Answer:
The number of moles of water in 1 L of water with density 1 g/cm³ is approximately **55.56 moles**.

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