Question

The molarity of pure water is: (a) \(55.56 \mathrm{M}\) (b) \(5.56 \mathrm{M}\) (c) \(1.0 \mathrm{M}\) (d) \(0.01 \mathrm{M}\)

Short answer

(a) 55.56 M

Step-by-step solution

Understand the Concept of Molarity

Molarity (M) is defined as the number of moles of solute per liter of solution. Since this question is asking for the molarity of pure water, water is considered both the solute and the solvent.

Calculate the Moles of Water

The molecular weight of water (H_2O) is approximately 18.015 g/mol. Assuming you have 1 liter of water, the density of water being approximately 1 g/mL, implies that 1 liter of water will have a mass of 1000 g.

Find the Number of Moles

Calculate the number of moles of water in 1000 g using the formula: \[ \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]Thus, \[ \text{moles of } H_2O = \frac{1000 \text{ g}}{18.015 \text{ g/mol}} \approx 55.56 \text{ moles} \]

Calculate Molarity

Now that we have the number of moles, we can determine the molarity of water. Since you calculated 55.56 moles in 1 liter of water, the molarity is: \[ Molarity = \frac{\text{moles of solute}}{\text{liter of solution}} = 55.56 \text{ M} \]

Choose the Correct Option

The calculated molarity of pure water is 55.56 M. Therefore, the correct option is (a) 55.56 M.

Key concepts

Calculation of Moles

Calculating the number of moles is a fundamental step in determining molarity. Moles represent a count of the number of molecules present in a given mass of a substance. To find the moles of water in 1000 g, use the formula:

• Formula: \( \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \)
• Example: For water, the calculation would be \( \frac{1000 \text{ g}}{18.015 \text{ g/mol}} \)

This results in approximately 55.56 moles of water in that 1-liter sample. Always ensure to know both the mass of your substance and its molar mass to compute moles accurately.

Molecular Weight of Water

Understanding the molecular weight (or molar mass) of water is crucial for various calculations in chemistry, particularly when dealing with solutions. Water, with its chemical formula \( H_2O \), has a molecular weight of approximately 18.015 g/mol. To derive this:

• Calculate the atomic masses of hydrogen and oxygen from the periodic table.
• Hydrogen has an atomic mass of about 1.008 g/mol. Since there are two hydrogens, multiply it by 2.
• Oxygen has an atomic mass of approximately 16.00 g/mol.
• Adding these values together gives: \( 2 \times 1.008 + 16.00 = 18.016 \) g/mol, generally rounded to 18.015 g/mol.

This molecular weight is vital for translating between mass and moles, especially in solution chemistry.

Density of Water

The density of water plays a significant role in converting between volume and mass. Density can be defined as mass per unit volume and is commonly expressed in g/mL for liquids like water. Since water has a density of approximately 1 g/mL, this tells us that each milliliter of water weighs about 1 gram. Therefore:

• 1 liter of water (which is 1000 mL) weighs 1000 grams.
• This property is critical when you need to determine the mass of a specific volume of water quickly.

Understanding this concept allows you to convert effortlessly between the mass and volume of water, a key skill in calculating molarity and other solution properties.