Problem 84 - Chemistry The Molecular Science

Question

Calculate the volume of 0.123 -M \(\mathrm{NaOH}\) that contains \(25.0 \mathrm{~g} \mathrm{NaOH}\). Express your result in milliliters.

Step-by-Step Solution

Answer

The volume required is 5080 mL.

Step 1: Determine the Molar Mass of NaOH

The molar mass of \(\mathrm{NaOH}\) can be calculated by adding the atomic masses of sodium \(\mathrm{(Na, 22.99\ g/mol)}\), oxygen \(\mathrm{(O, 16.00\ g/mol)}\), and hydrogen \(\mathrm{(H, 1.01\ g/mol)}\).\[\mathrm{Molar\ mass\ of\ NaOH} = 22.99\ g/mol + 16.00\ g/mol + 1.01\ g/mol = 40.00\ g/mol}\]

Step 2: Calculate Moles of NaOH

Using the mass of \(\mathrm{NaOH}\), we calculate the number of moles using the formula: Moles = mass/molar mass. Given that the mass is \(25.0\ g\), the number of moles is\[\text{Moles of NaOH} = \frac{25.0\ g}{40.00\ g/mol} = 0.625\ mol\]

Step 3: Use Molarity to Find Volume

We use the molarity formula to find the volume. Molarity (M) is defined as moles of solute per liter of solution: \(\text{Molarity} = \frac{\text{moles}}{\text{volume in liters}}\). Rearrange this to find volume: \(\text{Volume in liters} = \frac{\text{moles}}{\text{Molarity}}\). For a \(0.123\ M\) solution and \(0.625\ mol\):\[\text{Volume in liters} = \frac{0.625\ mol}{0.123\ M} = 5.08\ L\]

Step 4: Convert Liters to Milliliters

Convert the volume from liters to milliliters by using the conversion factor \(1000\ mL = 1\ L\):\[\text{Volume in milliliters} = 5.08\ L \times 1000\ mL/L = 5080\ mL\]

Key Concepts

Molarity

Molarity is a fundamental concept in chemistry that describes the concentration of a solution. It is defined as the number of moles of solute per liter of solution. Molarity is denoted by the symbol \(M\) and is used to convey how concentrated a solution is.

Understanding molarity helps chemists in preparing solutions with precision, essential for many chemical reactions. For a given solution, if you know the molarity and the volume, you can easily calculate the amount of solute present.

For instance, in our exercise, the molarity of the NaOH solution is given as 0.123 M. This indicates that there are 0.123 moles of NaOH in every liter of the solution. To find the volume of the solution needed to contain 0.625 moles of NaOH, we rearrange the molarity formula:

• \( \text{Volume in liters} = \frac{\text{moles}}{\text{Molarity}} \)

With 0.625 moles and a molarity of 0.123 M, the calculated volume is 5.08 liters, which is then converted to milliliters.

Molar Mass

Molar mass is a key concept in chemistry used to convert between the mass of a substance and the amount in moles. It is defined as the mass of one mole of a given substance and is usually expressed in grams per mole (g/mol). Calculating the molar mass involves adding together the atomic masses of all the elements in a compound.

In our NaOH example, the molar mass is calculated as follows:

• Sodium (Na): 22.99 g/mol
• Oxygen (O): 16.00 g/mol
• Hydrogen (H): 1.01 g/mol

The combined molar mass of NaOH is 40.00 g/mol. This means that one mole of sodium hydroxide weighs 40 grams.

In practice, knowing the molar mass allows us to determine the number of moles of a given mass of a substance. For example, using the molar mass of NaOH, we calculated that 25.0 grams of NaOH is equal to 0.625 moles.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between reactants and products in chemical reactions. It allows chemists to predict how much product will form based on the amount of reactants used.

In solution chemistry, stoichiometry often involves calculations using molarity, volume, and molar mass to find the amount of chemicals involved in a reaction. For example, our exercise is a straightforward application of stoichiometry: converting grams to moles and then using molarity to find the volume of solution needed.

Stoichiometry is crucial because it helps in:

• Calculating reactant concentrations and product yield
• Scaling reactions to desired product amounts
• Balancing chemical equations to maintain the conservation of mass

In essence, stoichiometry connects the world of measurable mass with the molecular handling of chemicals, guiding us through precise and reproducible chemical procedures.