Problem 142 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

In \(1200 \mathrm{~g}\) solution, \(12 \mathrm{~g}\) urea is present. If density of the solution is \(1.2 \mathrm{~g} / \mathrm{ml}\), then the molarity of the solution is (a) \(0.2 \mathrm{M}\) (b) \(10 \mathrm{M}\) (c) \(0.167 \mathrm{M}\) (d) \(12 \mathrm{M}\)

Step-by-Step Solution

Answer

0.167 M

Step 1: Calculate the number of moles of urea

Use the molar mass of urea to calculate the number of moles. The molar mass of urea (NH2CONH2) is approximately 60 g/mol. Use the formula: number of moles = mass of solute (g) / molar mass (g/mol).

Step 2: Calculate the volume of the solution in liters

Knowing the density of the solution and its mass, use the formula: volume (ml) = mass (g) / density (g/ml). Convert this volume to liters by dividing by 1000 since 1 L = 1000 mL.

Step 3: Calculate the molarity of the solution

Use the formula for molarity: molarity (M) = number of moles of solute / volume of solution in liters. Insert the number of moles from Step 1 and the volume in liters from Step 2 to get the molarity.

Key Concepts

Solution Concentration

Understanding solution concentration is essential when studying chemistry, as it describes the amount of a substance, known as the solute, dissolved in a given volume of solvent. This concentration can be expressed in various ways, including molarity, which is one of the most commonly used methods in chemistry. Molarity (M) is defined as the number of moles of solute per liter of solution. To calculate molarity, you need to know the volume of the solution in liters and the amount of solute in moles.

When dealing with real-life problems, calculating the molarity involves determining these two pieces of information. For instance, if you are given the mass of a solute and the mass and density of the solution, you can calculate molarity by converting the mass of solute to moles and the mass of the solution to volume in liters, accounting for the density.

Moles of Solute

The mole is a fundamental unit in chemistry that provides a bridge between the atomic scale and the macroscopic scale. It allows chemists to count particles (like atoms, molecules, ions) by weighing them. One mole of any substance contains approximately \( 6.022 \times 10^{23} \) entities (Avogadro's number). The number of moles of a solute is calculated by dividing the mass (in grams) of the solute by its molar mass (in grams per mole).

The step-by-step solution involved converting the given mass of urea into moles, which is a key step in finding the molarity. Understanding this conversion helps bypass confusion and ensures accuracy when calculating molar concentrations from mass-based measurements.

Molar Mass of Urea

The molar mass of a substance is the mass of one mole of that substance and is expressed in grams per mole (g/mol). Urea, with the chemical formula \((NH_2)_2CO\), is an organic compound often used in laboratories and industry. To find its molar mass, we add the atomic masses of all atoms in the formula: Nitrogen (N), Hydrogen (H), Carbon (C), and Oxygen (O).

The molar mass of urea is calculated as follows:\[2 \times 14.007\, \text{(N)} + 4 \times 1.008\, \text{(H)} + 12.011\, \text{(C)} + 15.999\, \text{(O)} \approx 60\, \text{g/mol}\]. Being able to calculate the molar mass allows chemists to convert between mass and moles, which is indispensable for preparing solutions and conducting stoichiometric calculations.

Concentration Units

Concentration units provide a means to express the composition of mixtures. Besides molarity, there are various units such as molality, mole fraction, percent composition by mass, and normality. Each unit serves a specific purpose and is selected based on the scenario.

Molarity, denoted as M, measures the number of moles of solute per liter of solution. Molality, on the other hand, measures the number of moles of solute per kilogram of solvent. Mole fraction is the ratio of the number of moles of one component to the total number of moles in the solution. Percent composition by mass is simply the percentage of the mass of each component relative to the total mass of the mixture. Normality, used in acid-base chemistry, is the number of equivalents of a substance per liter of solution. Understanding these units and when to use them is crucial for precise communication in scientific contexts.