Calculate molarity of water if its density is 1.00 g `mL^(-1)`.

Answer

To calculate the molarity of water given its density, we can follow these steps:

### Step 1: Understand the Definition of Molarity
Molarity (M) is defined as the number of moles of solute per liter of solution. The formula for molarity is:
\[ \text{Molarity (M)} = \frac{\text{Number of moles of solute}}{\text{Volume of solution in liters}} \]

### Step 2: Determine the Density of Water
The density of water is given as 1.00 g/mL. This means that 1 mL of water has a mass of 1 gram.

### Step 3: Convert Density to Mass per Liter
Since there are 1000 mL in a liter, we can convert the density to find the mass of water in one liter:
\[ \text{Mass of water in 1 liter} = 1 \, \text{g/mL} \times 1000 \, \text{mL} = 1000 \, \text{g} \]

### Step 4: Calculate the Number of Moles of Water
To find the number of moles of water, we use the formula:
\[ \text{Number of moles} = \frac{\text{Mass of water}}{\text{Molar mass of water}} \]
The molar mass of water (H₂O) is approximately 18 g/mol. Therefore:
\[ \text{Number of moles of water} = \frac{1000 \, \text{g}}{18 \, \text{g/mol}} \approx 55.56 \, \text{moles} \]

### Step 5: Calculate Molarity
Now that we have the number of moles of water and the volume of the solution in liters, we can calculate the molarity:
\[ \text{Molarity} = \frac{55.56 \, \text{moles}}{1 \, \text{L}} = 55.56 \, \text{M} \]

### Final Answer
The molarity of water is approximately **55.56 M**.

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