Number of moles of water in 1L of `H_(2)O` with density `1g//cm^(3)` are

Options

A. 55.56
B. 45.56
C. 56.55
D. 56.45

Explanation

To find the number of moles of water in 1 liter of \( H_2O \) with a density of \( 1 \, \text{g/cm}^3 \), we can follow these steps:

### Step 1: Understand the relationship between density, mass, and volume.
The formula for density (\( \rho \)) is given by:
\[ \rho = \frac{\text{mass}}{\text{volume}} \]
From this, we can rearrange the formula to find the mass:
\[ \text{mass} = \rho \times \text{volume} \]

### Step 2: Convert the volume from liters to cubic centimeters.
We know that:
\[ 1 \, \text{liter} = 1000 \, \text{cm}^3 \]
So, the volume of water we are considering is:
\[ \text{volume} = 1000 \, \text{cm}^3 \]

### Step 3: Calculate the mass of water using the density.
Given that the density of water is \( 1 \, \text{g/cm}^3 \):
\[ \text{mass} = 1 \, \text{g/cm}^3 \times 1000 \, \text{cm}^3 = 1000 \, \text{g} \]

### Step 4: Use the molar mass of water to find the number of moles.
The molar mass of water (\( H_2O \)) is approximately \( 18 \, \text{g/mol} \). The number of moles (\( n \)) can be calculated using the formula:
\[ n = \frac{\text{mass}}{\text{molar mass}} \]
Substituting the values we have:
\[ n = \frac{1000 \, \text{g}}{18 \, \text{g/mol}} \approx 55.56 \, \text{moles} \]

### Final Answer:
The number of moles of water in 1 liter of \( H_2O \) is approximately \( 55.56 \, \text{moles} \).

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