To find the molality of water given its density, we can follow these steps:
### Step 1: Understand the definition of molality
Molality (m) is defined as the number of moles of solute per kilogram of solvent. In this case, we are considering water as the solvent.
### Step 2: Use the density to find the mass of water
Given the density of water (ρ) is 1000 kg/m³, we can calculate the mass of water for a specific volume. We will consider a volume of 1 liter (which is equivalent to 0.001 m³).
Using the formula for density:
\[
\rho = \frac{mass}{volume}
\]
We can rearrange this to find mass:
\[
mass = \rho \times volume
\]
Substituting the values:
\[
mass = 1000 \, \text{kg/m}^3 \times 0.001 \, \text{m}^3 = 1 \, \text{kg}
\]
### Step 3: Calculate the number of moles of water
Next, we need to calculate the number of moles of water. The molar mass of water (H₂O) is calculated as follows:
- Hydrogen (H) has a molar mass of approximately 1 g/mol, and there are 2 hydrogen atoms in water.
- Oxygen (O) has a molar mass of approximately 16 g/mol.
Thus, the molar mass of water is:
\[
\text{Molar mass of H}_2\text{O} = (2 \times 1) + 16 = 18 \, \text{g/mol}
\]
Now, we can find the number of moles of water using the formula:
\[
\text{Number of moles} = \frac{mass}{molar mass}
\]
Substituting the values:
\[
\text{Number of moles} = \frac{1000 \, \text{g}}{18 \, \text{g/mol}} \approx 55.56 \, \text{moles}
\]
### Step 4: Calculate molality
Now that we have the number of moles of water and the mass of the solvent (water), we can calculate molality:
\[
\text{Molality} = \frac{\text{Number of moles of solute}}{\text{Mass of solvent in kg}}
\]
Since we are considering pure water as the solvent, the number of moles of solute is the number of moles of water calculated above:
\[
\text{Molality} = \frac{55.56 \, \text{moles}}{1 \, \text{kg}} = 55.56 \, \text{mol/kg}
\]
### Step 5: Round the answer
Finally, we round the answer to one decimal place:
\[
\text{Molality} \approx 55.6 \, \text{mol/kg}
\]
### Final Answer:
The molality of water is **55.6 mol/kg**.
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