Problem 26 - Chemistry A Molecular Approach

Question

What volume of \(0.200 \mathrm{M}\) ethanol solution contains eacl amount in moles of ethanol? a. 0.45 mol ethanol b. 1.22 mol ethanol c. \(1.2 \times 10^{-2}\) mol ethanol

Step-by-Step Solution

Answer

The volumes of 0.200 M ethanol solution are: a. 2.25 liters, b. 6.10 liters, and c. \(6.0 \times 10^{-2}\) liters.

Step 1: Understand the concept of molarity

Molarity (M) is defined as the number of moles of solute (in this case, ethanol) divided by the volume of solution in liters. The formula for molarity is M = moles of solute / liters of solution.

Step 2: Calculate the volume for 0.45 mol of ethanol

Using the molarity formula, rearrange to solve for the volume of solution. Volume = moles of solute / Molarity. For 0.45 mol ethanol in a 0.200 M solution: Volume = 0.45 mol / 0.200 M.

Step 3: Calculate the volume for 1.22 mol of ethanol

Applying the same method as in Step 2, for 1.22 mol ethanol in a 0.200 M solution: Volume = 1.22 mol / 0.200 M.

Step 4: Calculate the volume for \(1.2 \times 10^{-2}\) mol of ethanol

Again, using the same method for \(1.2 \times 10^{-2}\) mol ethanol in a 0.200 M solution: Volume = \(1.2 \times 10^{-2}\) mol / 0.200 M.

Step 5: Perform the calculations

For Step 2: Volume = 0.45 mol / 0.200 M = 2.25 liters.For Step 3: Volume = 1.22 mol / 0.200 M = 6.10 liters.For Step 4: Volume = \(1.2 \times 10^{-2}\) mol / 0.200 M = \(6.0 \times 10^{-2}\) liters.

Key Concepts

Molarity

Molarity is a crucial concept when it comes to expressing the concentration of a solution. It is officially denoted as 'M' and defined as the number of moles of solute dissolved per liter of solution. This relationship offers a straightforward method for communicating how concentrated or dilute a solution is.

One mole of a substance contains Avogadro's number of entities (atoms, molecules, ions, etc.), which is approximately equal to 6.022 x 10²³ entities. Therefore, when we say a solution has a molarity of 1 M, it means it contains one mole of the solute in one liter of solution. This becomes very helpful in chemical reactions and laboratory calculations where precise amounts of substances are required.

To calculate molarity, we use the formula: \( M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \).

Volume of Solution

In molarity calculations, the volume of solution plays a critical role. To find out how much solution you need or have, you work with the volume, which is typically measured in liters in the context of molarity. A liter is a unit of volume equal to 1,000 milliliters (mL) or 1,000 cubic centimeters (cm³).

There are scenarios, especially in a laboratory setting, where knowing the volume that contains a particular amount of solute is important. When you're given the moles of solute and the molarity of the solution, you can easily calculate the volume needed. For this, you rearrange the molarity equation to solve for volume: \( \text{Volume} = \frac{\text{moles of solute}}{\text{Molarity}} \).

Using this formula helps to prepare solutions with precise concentrations or to dilute a stock solution to a desired concentration by adding an appropriate amount of solvent.

Moles of Solute

The concept of 'moles of solute' is a measure of the actual amount of a substance present in a solution. Since the molarity depends on the amount of the solute, identifying moles is vital in stoichiometry and chemistry calculations.

One mole of any substance is equal to its molecular weight in grams, which corresponds to Avogadro's number of molecules or atoms, depending on the type of substance. For instance, if the molecular weight of ethanol (C₂H₅OH) is about 46.07 g/mol, then 46.07 grams of ethanol represent 1 mole.

Therefore, in molarity calculations, counting the moles of the solute lets us establish a link between the mass and the number of particles in the solution. This is particularly useful when you need to relate the physical mass of a substance to the number of particles required for a chemical reaction (stoichiometry).