Problem 32 - Chemistry in 30 days

Question

How many grams of \(\mathrm{CH}_{3} \mathrm{OH}\) would have to be added to water to prepare \(150 \mathrm{ml}\) of a solution that is \(2.0 \mathrm{M} \mathrm{CH}_{3} \mathrm{OH}\) ? (a) \(9.6\) (b) \(2.4\) (c) \(9.6 \times 10^{3}\) (d) \(4.3 \times 10^{2}\)

Step-by-Step Solution

Answer

You need to add 9.6 grams of \( \mathrm{CH}_3 \mathrm{OH} \) to the water.

Step 1: Understand the Problem

We are tasked with preparing a solution with a specific molarity (M). Molarity is defined as the number of moles of solute per liter of solution. We need to calculate how many grams of methanol (\( \mathrm{CH}_3 \mathrm{OH} \)) are required for a \( 2.0 \mathrm{M} \) solution with a volume of \( 150 \mathrm{ml} \).

Step 2: Convert Volume to Liters

Molarity requires the volume of the solution in liters. Convert \( 150 \mathrm{ml} \) into liters, since \( 1 \mathrm{L} = 1000 \mathrm{ml} \). So, \( 150 \mathrm{ml} = 0.150 \mathrm{L} \).

Step 3: Calculate Moles of \( \mathrm{CH}_3 \mathrm{OH} \) Required

Use the molarity formula: \( M = \frac{\text{moles of solute}}{\text{liters of solution}} \). Given \( M = 2.0 \mathrm{M} \) and \( 0.150 \mathrm{L} \) of solution, calculate the moles of \( \mathrm{CH}_3 \mathrm{OH} \). Moles = \( 2.0 \mathrm{M} \times 0.150 \mathrm{L} = 0.300 \text{ moles} \).

Step 4: Molar Mass Calculation

Calculate the molar mass of \( \mathrm{CH}_3 \mathrm{OH} \). The atomic weights are: C = 12.01, H = 1.01, and O = 16.00. So, the molar mass is \( 12.01 + (4 \times 1.01) + 16.00 = 32.05 \text{ g/mol} \).

Step 5: Convert Moles to Grams

Now, convert the moles of \( \mathrm{CH}_3 \mathrm{OH} \) to grams using its molar mass: \( 0.300 \text{ moles} \times 32.05 \text{ g/mol} = 9.615 \text{ grams} \).

Step 6: Choosing the Nearest Option

Compare the calculated mass to the provided options; option (a) \( 9.6 \) grams matches, considering rounding.

Key Concepts

solution preparation

When preparing a chemical solution, it is important to understand the concept of solution preparation. This involves dissolving a specific amount of a solute into a solvent to achieve the desired concentration. In this example, the solute is methanol (\(\mathrm{CH}_3 \mathrm{OH}\)) and the solvent is water.

• Start by determining the target molarity, which is the concentration of solute expressed in moles per liter.
• Next, calculate the volume of the solution you wish to prepare in liters. In this case, the volume is initially given in milliliters and needs to be converted to liters.

Finally, calculate the amount of solute you need by using the formula \(\text{moles of solute} = \text{molarity} \times \text{volume of solution in liters}\). This step ensures you are adding the exact quantity of solute required to achieve the specified molarity.

mole concept

The mole concept is a fundamental idea in chemistry used to quantify the amount of substance. One mole of any substance contains \(\approx 6.022 \times 10^{23}\) entities, which is known as Avogadro's number.

• It provides a bridge between the atomic scale and macroscopic amount of a chemical substance.
• In our case, we need to understand how many moles of methanol are needed for the solution.

By calculating the number of moles, we relate the measurable volume to the amount of substance utilizing the molarity formula. Thus, understanding the mole concept allows us to easily convert between moles, mass, and molecules.

chemical calculations

Chemical calculations often involve converting quantities from one form to another using mathematical relationships. To solve problems, you perform conversions such as volume to moles, and moles to mass.

• Begin with understanding what is known (e.g., molarity and volume) and what needs to be found (e.g., mass).
• Use the appropriate formulas, such as \(M = \dfrac{\text{moles of solute}}{\text{liters of solution}}\) to find the necessary moles of solute.

The goal is to connect each step logically, verifying that each value and unit conversion contributes to the final solution. This ensures accurate and reliable chemical calculations.

molar mass determination

Determining the molar mass of a compound is crucial for various calculations, including converting moles to grams.

• Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol).
• Calculate it by summing the atomic masses of all atoms in the chemical formula.

For methanol (\(\mathrm{CH}_3 \mathrm{OH}\)), calculate using the atomic masses: Carbon (C) is 12.01 g/mol, Hydrogen (H) is 1.01 g/mol, and Oxygen (O) is 16.00 g/mol. Add these together based on the number of each atom present to find the molar mass. In this case, it is \(32.05\) g/mol, essential for converting the number of moles to grams accurately.