The molarity of 648 g of pure water is

Options

A. 36 m
B. 55.5 m
C. 3.6 m
D. 5.55 m

Answer

To find the molarity of 648 g of pure water, we can follow these steps:

### Step 1: Understand the concept of molarity
Molarity (M) is defined as the number of moles of solute per liter of solution. In this case, we are considering pure water, which means that the solute is water itself.

### Step 2: Calculate the volume of water
Given that the density of water is 1 g/cm³, we can convert the mass of water to volume:
- Mass of water = 648 g
- Volume of water = Mass / Density = 648 g / (1 g/cm³) = 648 cm³

Now, convert the volume from cm³ to liters:
- Volume in liters = 648 cm³ × (1 L / 1000 cm³) = 0.648 L

### Step 3: Calculate the number of moles of water
To find the number of moles of water, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass of water (g)}}{\text{molar mass of water (g/mol)}} \]

The molar mass of water (H₂O) is calculated as follows:
- H: 1 g/mol × 2 = 2 g/mol
- O: 16 g/mol
- Total molar mass of H₂O = 2 + 16 = 18 g/mol

Now, calculate the number of moles:
\[ \text{Number of moles} = \frac{648 \text{ g}}{18 \text{ g/mol}} = 36 \text{ moles} \]

### Step 4: Calculate the molarity
Now we can calculate the molarity using the formula:
\[ M = \frac{\text{Number of moles}}{\text{Volume of solution (L)}} \]

Substituting the values we found:
\[ M = \frac{36 \text{ moles}}{0.648 \text{ L}} \]

Calculating this gives:
\[ M = 55.55 \text{ mol/L} \]

### Final Answer
The molarity of 648 g of pure water is **55.55 M**.

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