Question

Calculate the volume in milliliters of a solution required to provide the following: (a) \(2.14 \mathrm{~g}\) of sodium chloride from a \(0.270-M\) solution, (b) \(4.30 \mathrm{~g}\) of ethanol from a \(1.50-M\) solution, (c) \(0.85 \mathrm{~g}\) of acetic acid \(\left(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\right)\) from a \(0.30-M\) solution.

Short answer

(a) 135.6 mL, (b) 62.2 mL, (c) 47.3 mL

Step-by-step solution

Calculate Moles of Solute

To find the volume required, we must first determine the number of moles of solute. Use the formula \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \). For each compound, we need its molar mass.

Find Molar Mass and Moles for Sodium Chloride

The molar mass of NaCl is approximately \(58.44 \text{g/mol}\). For a mass of \(2.14 \text{g}\), the moles are \( \frac{2.14}{58.44} \approx 0.0366 \text{ moles} \).

Calculate Volume for Sodium Chloride Solution

Use the formula \( V = \frac{\text{moles}}{\text{molarity}} \). For NaCl, \( V = \frac{0.0366}{0.270} \approx 0.1356 \text{ L} \), which converts to \(135.6 \text{ mL}\).

Find Molar Mass and Moles for Ethanol

The molar mass of ethanol (C\(_2\)H\(_5\)OH) is approximately \(46.08 \text{g/mol}\). For a mass of \(4.30 \text{g}\), the moles are \( \frac{4.30}{46.08} \approx 0.0933 \text{ moles} \).

Calculate Volume for Ethanol Solution

Using \( V = \frac{\text{moles}}{\text{molarity}} \), for ethanol, \( V = \frac{0.0933}{1.50} \approx 0.0622 \text{ L} \), which converts to \(62.2 \text{ mL}\).

Find Molar Mass and Moles for Acetic Acid

The molar mass of acetic acid (HC\(_2\)H\(_3\)O\(_2\)) is approximately \(60.05 \text{g/mol}\). For a mass of \(0.85 \text{g}\), the moles are \( \frac{0.85}{60.05} \approx 0.0142 \text{ moles} \).

Calculate Volume for Acetic Acid Solution

Using \( V = \frac{\text{moles}}{\text{molarity}} \), for acetic acid, \( V = \frac{0.0142}{0.30} \approx 0.0473 \text{ L} \), which converts to \(47.3 \text{ mL}\).

Key concepts

Molarity

Molarity is a crucial concept in chemistry that measures the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution, often represented as \( M = \frac{\text{moles of solute}}{\text{liters of solution}} \).
Understanding molarity is vital for preparing solutions of precise concentrations, essential in experiments where accurate measurement is critical.

• A higher molarity means a more concentrated solution.
• A lower molarity indicates a more dilute solution.

When working with solutions, molarity helps chemists decipher how much solute is present in a given volume of solvent.
This understanding is a cornerstone of solution stoichiometry, enabling precise control and predictability in reactions.

Molar Mass

Molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). It is obtained by summing the atomic masses of all atoms in a molecule, based on their amounts from the periodic table.
Knowing the molar mass of a substance is essential for converting between the mass of a substance and the number of moles.

• The molar mass of sodium chloride (NaCl) is approximately 58.44 g/mol.
• Ethanol (C\(_2\)H\(_5\)OH) has a molar mass of about 46.08 g/mol.
• Acetic acid (HC\(_2\)H\(_3\)O\(_2\)) has a molar mass of about 60.05 g/mol.

This conversion is essential for calculating the moles of solute in solution stoichiometry problems.

Solution Preparation

Solution preparation involves creating a solution with a specific molarity. This process requires careful calculation and measurement to ensure the correct concentration.

• First, the amount of solute needed is determined by calculating the moles using its molar mass.
• The required volume of solution is calculated, taking into account the desired molarity.

The formula to find the volume of solution needed is \( V = \frac{\text{moles of solute}}{\text{molarity}} \).
This step is crucial for experiments that demand accuracy, as the properties and outcome of a reaction can depend heavily on solute concentration.

Moles Calculation

Calculating moles is foundational in chemistry for quantifying substances. Moles represent the amount of a substance and provide a bridge between the atomic scale and the macroscopic world.
The basic formula for calculating moles is \( \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \).

• This formula allows conversion from the mass of a substance to the number of moles it contains.
• Knowing the amount in moles is crucial before proceeding with stoichiometry calculations.

These calculations are pivotal in determining the exact quantities for chemical reactions and solution preparations, ensuring precise scientific measurements.