Question

Rubbing alcohol contains \(585 \mathrm{~g}\) isopropanol \(\left(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}\right)\) per liter (aqueous solution). Calculate the molarity.

Short answer

The molar mass of isopropanol is \(M_\text{C3H7OH} = 3(12.01) + 8(1.01) + 1(16.00) = 60.10 \text{ g/mol}\). Next, calculate the moles of isopropanol: \(\text{moles} = \frac{585 \text{ g}}{60.10 \text{ g/mol}} = 9.74 \text{ mol}\). Finally, calculate the molarity: \(\text{Molarity} = \frac{9.74 \text{ mol}}{1 \text{ L}} = 9.74 \text{ M}\).

Step-by-step solution

Determine the molar mass of isopropanol

The first step is to determine the molar mass of isopropanol, C3H7OH. The formula contains 3 carbon atoms, 8 hydrogen atoms, and 1 oxygen atom. Using the periodic table, we can find the atomic masses of carbon (C), hydrogen (H), and oxygen (O) as follows: \[M_\text{C} = 12.01 \text{ g/mol}\] \[M_\text{H} = 1.01 \text{ g/mol}\] \[M_\text{O} = 16.00 \text{ g/mol}\] Now, we can calculate the molar mass of isopropanol: \[M_\text{C3H7OH} = 3M_\text{C} + 8M_\text{H} + 1M_\text{O}\]

Calculate the moles of isopropanol

Next, we need to calculate the number of moles of isopropanol in the solution. We are given that there are 585 g of isopropanol in 1 L of the solution. We can convert this mass into moles using the molar mass of isopropanol: \[\text{moles of isopropanol} = \frac{\text{mass of isopropanol}}{\text{molar mass of isopropanol}}\]

Calculate the molarity

Finally, we can calculate the molarity of the solution by dividing the number of moles of isopropanol by the volume of the solution in liters: \[\text{Molarity} = \frac{\text{moles of isopropanol}}{\text{volume in liters}}\] We already have the number of moles (from step 2) and the volume (1 L) of the solution. Simply substitute the values and calculate the molarity.

Key concepts

Molar Mass

Understanding molar mass is essential when working with chemical substances. Molar mass is the mass of one mole of a given substance. It is usually expressed in grams per mole (g/mol). To find the molar mass of a compound like isopropanol \( \text{C}_3\text{H}_7\text{OH} \), add up the molar masses of all the atoms present in the molecule.
The molar mass of elements can be found on the periodic table:

• Carbon (C) = 12.01 g/mol
• Hydrogen (H) = 1.01 g/mol
• Oxygen (O) = 16.00 g/mol

For isopropanol, calculate its molar mass using the formula: \[ \text{Molar Mass of C}_3\text{H}_7\text{OH} = 3 \times 12.01 + 8 \times 1.01 + 16.00 = 60.10\ \text{g/mol} \] This means that the mass of one mole of isopropanol is 60.10 grams. Calculating the molar mass helps you determine how many moles are in a given mass of a substance.

Isopropanol

Isopropanol, also known as isopropyl alcohol or \( \text{C}_3\text{H}_7\text{OH} \), is a common chemical compound used in various applications. It's often found in rubbing alcohol solutions and is known for its antiseptic properties, making it useful for cleaning and sanitizing.

Some important characteristics of isopropanol include:

• It is a colorless liquid with a strong alcoholic odor.
• It evaporates quickly at room temperature, making it effective for disinfection.
• It is miscible with water, meaning it can mix with water in any proportion.

Understanding the properties of isopropanol can help predict its behavior, especially in solutions like the one described in the exercise. Its miscibility with water makes it easy to form homogenous mixtures, which is why it's used as a solvent in many chemical applications.

Chemical Solution

Solutions are homogeneous mixtures consisting of two or more substances. In chemistry, a solution typically consists of a solute and a solvent. The solute is the substance dissolved, whereas the solvent is the dissolving medium. In the given exercise, isopropanol is the solute, while the water in which it's dissolved acts as the solvent.

Key characteristics of chemical solutions include:

• Uniform composition throughout.
• Cannot be separated by physical means, like filtration.
• Molarity, often used to express concentration, is the number of moles of solute per liter of solution.

Molarity allows chemists to express concentrations of various components in a solution in a simple, unified manner. To find the molarity of this exercise, divide the moles of isopropanol by the liters of solution. For instance, if you have the moles calculated and a 1-liter solution, it's straightforward to use \[ \text{Molarity} = \frac{\text{moles of solute}}{\text{liters of solution}} \] This calculation lets you understand the strength of the solution and is crucial for conducting experiments accurately.