Problem 11 - Chemistry An Atoms First Approach

Question

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

Step-by-Step Solution

Answer

The molar mass of isopropanol (C3H7OH) is calculated as follows: Molar mass = 3 × (12.01 g/mol) + 7 × (1.01 g/mol) + 16.00 g/mol + 1.01 g/mol = 60.10 g/mol The moles of isopropanol in 1 L of rubbing alcohol is given by: Moles = \(\frac{585~g}{60.10~g/mol}\) = 9.74 mol Finally, the molarity is calculated as: Molarity = \(\frac{9.74~mol}{1~L}\) = 9.74 M

Step 1: Calculate the molar mass of isopropanol (C3H7OH)

First, we need to find the molar mass of isopropanol. Each element in the molecule has a specific atomic mass: - Carbon (C): \(12.01 g/mol\) - Hydrogen (H): \(1.01 g/mol\) - Oxygen (O): \(16.00 g/mol\) The formula for isopropanol is C3H7OH, so its molar mass can be calculated as follows: Molar mass of isopropanol = 3 × (molar mass of C) + 7 × (molar mass of H) + (molar mass of O) + (molar mass of H)

Step 2: Find the moles of isopropanol

Given that rubbing alcohol contains 585 g of isopropanol per liter, we can now use the molar mass of isopropanol to calculate the number of moles in 1 liter of the solution: Moles of isopropanol = \(\frac{mass}{molar~mass}\)

Step 3: Calculate the molarity

Finally, we can use the definition of molarity to determine the molarity of the rubbing alcohol solution: Molarity = \(\frac{moles~of~solute}{volume~of~solution~(in~liters)}\) Plug in the values and compute the molarity.

Key Concepts

Isopropanol Molarity

Understanding the molarity of isopropanol is crucial when dealing with solutions in chemistry. Molarity, a measure of concentration, explains how many moles of a solute are present in a liter of solution. It's represented by the symbol 'M' and is calculated using the equation:

Molarity (M) = \( \frac{\text{moles of solute}}{\text{volume of solution in liters}} \).

For isopropanol, which is commonly found in rubbing alcohol, determining its molarity involves knowing the mass of isopropanol dissolved and the volume of the solution. This concept is widely used in laboratory settings to prepare solutions of precise concentrations for experiments and titrations. In your studies, not only should you learn how to compute molarity, but also gain an understanding of how it applies to real-world scenarios and affects the properties of the solution.

Molar Mass Calculation

The molar mass calculation is a fundamental step to many chemistry problems, including finding the concentration of a solution. To calculate the molar mass of a compound like isopropanol (\( C_{3}H_{7}OH \)), you'll need to sum the atomic masses of each atom in the molecule. This might seem tricky, but it's a simple addition once you know the atomic mass of carbon, hydrogen, and oxygen from the periodic table:

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

With these values, calculate the molar mass by multiplying the quantity of each atom with its atomic mass and add them up. The molar mass is essential for converting between grams and moles, which is a necessary step for finding the molarity.

Moles of Solute

The term 'moles of solute' refers to the amount of a substance (solute) present in a solution. To find the moles of a substance like isopropanol in a solution, use the formula:

Moles = \(\frac{\text{mass of the solute}}{\text{molar mass}}\)

For isopropanol, you would divide the given mass in the solution by its molar mass. Moles are part of the foundation of stoichiometry, the area of chemistry that deals with the relative quantities of reactants and products in chemical reactions. A deep understanding of moles is not just about number crunching; it's about comprehending the concept of 'amount of substance' which is a bridge between the macroscopic world we observe and the microscopic world of atoms and molecules.

Concentration of Solution

The concentration of a solution tells how much solute is dissolved in a specific amount of solvent. It’s a measure of the 'strength' or 'intensity' of the solution. Concentration can be expressed in various ways, including molarity, molality, and parts per million, among others.

When discussing molarity, the concentration is defined by the number of moles of solute per liter of solution. This measurement is intrinsic to the preparation of solutions in the lab and is crucial in fields like analytical chemistry, where precise measurements lead to accurate results. Understanding concentrations is not only about mathematical computations but also about getting insights into how different concentrations affect chemical reactivity, solution properties, and the outcome of scientific experiments.