Problem 47 - Chemistry The Molecular Nature of Matter

Question

Calculate the molar concentration of water in (a) \(18.0 \mathrm{~mL}\) of \(\mathrm{H}_{2} \mathrm{O}(l),\) (b) \(100.0 \mathrm{~mL}\) of \(\mathrm{H}_{2} \mathrm{O}(l),\) and \(\mathbf{( c )} 1.00 \mathrm{~L}\) of \(\mathrm{H}_{2} \mathrm{O}(l)\). Assume that the density of water is \(1.00 \mathrm{~g} / \mathrm{mL}\)

Step-by-Step Solution

Answer

The molar concentrations are (a) approximately 55.5 M, (b) approximately 55.5 M, and (c) approximately 55.5 M.

Step 1: Convert volume to mass

Using the density of water, which is 1.00 g/mL, convert the volume of water to mass for each scenario since 1 mL of water has a mass of 1 g. For (a) 18.0 mL of water, the mass is 18.0 g. For (b) 100.0 mL of water, the mass is 100.0 g. For (c) 1.00 L (1000 mL) of water, the mass is 1000 g.

Step 2: Calculate the number of moles of water

Using the molar mass of water, which is approximately 18.015 g/mol, calculate the number of moles. The formula to find moles is mass (g) ÷ molar mass (g/mol). For (a) 18.0 g, the moles are 18.0 g ÷ 18.015 g/mol. For (b) 100.0 g, the moles are 100.0 g ÷ 18.015 g/mol. For (c) 1000 g, the moles are 1000 g ÷ 18.015 g/mol.

Step 3: Calculate molar concentration

Molar concentration (M) is calculated as moles of solute divided by liters of solution. For (a) we have the moles from Step 2 and volume in liters (0.018 L), so concentration is moles/0.018 L. For (b) concentration is moles/0.100 L, and for (c) moles/1.00 L.

Step 4: Express the result for each case

Calculate the concentration for each case and express it in M (molarity), which is moles per liter. For (a), divide the moles of water by 0.018 L, for (b), divide by 0.100 L, and for (c), divide by 1.00 L.

Key Concepts

Molecular Mass of Water

Understanding the molecular mass of water (H₂O) is vital in various chemical calculations. The molecular mass corresponds to the combined mass of all atoms within a molecule.

For water, each molecule contains two hydrogen atoms and one oxygen atom. Hydrogen has an atomic mass of approximately 1.008 amu (atomic mass units), and oxygen has an atomic mass of about 16.00 amu. Therefore, the molecular mass of a water molecule is calculated as follows: 2(1.008 amu) + 16.00 amu, which gives approximately 18.016 amu. In grams per mole, this value is almost the same, 18.015 g/mol, as this is the international standard for expressing molar mass.

Converting Mass to Moles

One of the most fundamental skills in chemistry is converting mass to moles. This process allows for the quantification of substances based on the molar mass. To convert mass to moles, you simply divide the mass of the substance by its molar mass.

The formula is:
\[ \text{Number of moles} = \frac{\text{Mass of substance (g)}}{\text{Molar mass (g/mol)}} \]
For instance, given the mass of water and its molar mass (18.015 g/mol), we can calculate the number of moles of water by dividing the mass by the molar mass. This step is crucial in preparing solutions and for molar concentration calculations.

Calculating Molarity

Molarity, denoted as M, is an expression of concentration in terms of mole of solute per liter of solution. It's a critical concept for understanding solution chemistry and is widely used in scientific and industrial applications. To calculate molarity, use the formula:
\[ \text{Molarity (M)} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}} \]

For any amount of water, first calculate the moles, as shown in the previous section. Then, divide this value by the volume of water in liters to get the molarity. This calculation assumes the volume doesn't change significantly when the solute dissolves, which is usually the case with dilute solutions like water.