Problem 174 - A Complete Resource Book in Chemistry for JEE Main

Question

The density (in \(\mathrm{g} \mathrm{mL}^{-1}\) ) of a \(3.60 \mathrm{M}\) sulphuric acid solution, that is, \(29 \% \mathrm{H}_{2} \mathrm{SO}_{4}\) (molar mass \(=98 \mathrm{~g}\) \(\mathrm{mol}^{-1}\) ) by mass will be \([\mathbf{2 0 0 7}]\) (a) \(1.88\) (b) \(1.22\) (c) \(1.45\) (d) \(1.64\)

Step-by-Step Solution

Answer

The density of the solution is approximately 1.22 g/mL.

Step 1: Understand the given data

We are given a sulphuric acid solution that is 29% by mass and has a molarity of 3.60 M. Our goal is to find the density of the solution. We'll utilize the molar mass of sulphuric acid (\(\text{H}_2\text{SO}_4\)) which is 98 \(\text{g mol}^{-1}\), and express the volume and mass of the solution in terms of these details.

Step 2: Set up the relationship between mass, molarity, and volume

First, let's restate molarity, which is defined as the number of moles of solute (here, H\(_2\)SO\(_4\)) per liter of solution. Using 1 liter of solution, the number of moles of H\(_2\)SO\(_4\) is calculated as \(3.60 \text{ moles/L} \times 1 \text{ L} = 3.60 \text{ moles}\).

Step 3: Calculate the mass of H\(_2\)SO\(_4\) in the solution

The mass of the sulphuric acid in the solution can be found using its molar mass. This is calculated as:\[\text{mass of } \text{H}_2\text{SO}_4 = \text{number of moles} \times \text{molar mass} = 3.60 \text{ moles} \times 98 \text{ g/mol} = 352.8 \text{ g.}\]

Step 4: Calculate the total mass of the solution

Using the given percentage by mass of sulphuric acid (29%), we can express this relationship as: \[\frac{\text{mass of } \text{H}_2\text{SO}_4}{\text{total mass of solution}} = 0.29\] Let "total mass" be represented by \(m_{\text{total}}\). Thus, \[352.8 = 0.29 \times m_{\text{total}}\] Solving for \(m_{\text{total}}\), we find \[m_{\text{total}} = \frac{352.8}{0.29} \approx 1216.55 \text{ g.}\]

Step 5: Calculate the density of the solution

Density is defined as mass per unit volume. Therefore, \[\text{Density} = \frac{\text{total mass of solution}}{\text{volume of solution}} = \frac{1216.55 \text{ g}}{1000 \text{ mL}} = 1.217 \text{ g/mL.}\] The closest value to this is option (b), which is 1.22.

Key Concepts

Sulphuric Acid Solution

The sulphuric acid solution mentioned here is a mixture of water and sulphuric acid (H\(_2\)SO\(_4\)). Sulphuric acid is a strong mineral acid, known for its high reactivity and corrosive nature. This solution is categorized as 29% by mass, meaning that out of 100 grams of the solution, 29 grams are pure sulphuric acid. This information helps us understand the weight of the acid present within the total mass of the solution. High concentrations of sulphuric acid in solutions can lead to notable rates of reaction when used in chemical experiments due to its strong acidic properties. When handling such solutions, always consider safety precautions due to the hazardous nature of the substance.

Molarity

Molarity is a measure of concentration used in chemistry. It shows how many moles of a solute are present in one liter of solution. In the exercise, the molarity is given as 3.60 M, meaning there are 3.60 moles of sulphuric acid in every liter of the solution. Calculating molarity involves dividing the number of moles of solute by the volume of solution in liters, which reinforces its use as a practical measurement of concentration in laboratory and industrial settings. Molarity enables precise control over the concentrations of chemical solutions, essential for accurate and replicable experiments.

Percentage by Mass

Percentage by mass is a way of expressing the concentration of an element in a compound or a component in a mixture. It is given in terms of the mass of the solute divided by the total mass of the solution, multiplied by 100%. In the exercise, the sulphuric acid solution is 29% by mass, indicating that sulphuric acid constitutes 29% of the solution's total mass. This form of concentration measurement is significant in situations where mixing and reactions are affected primarily by the mass of the components rather than their chemical entities. The information of percentage by mass helps in assessing how much of a substance is present in a given weight of mixture, useful in industrial applications and formulations.

Molar Mass

Molar mass is a fundamental property of any given chemical substance, defined as the mass of one mole of its atoms or molecules, expressed in grams per mole (g/mol). For sulphuric acid, the molar mass is 98 g/mol. This means that one mole of sulphuric acid weighs 98 grams. Using molar mass, chemists convert between the mass of a substance and the amount of substance (in moles), which is particularly useful in chemical calculations for balancing reactions, determining yields, and preparing solutions with precise molarities. An accurate understanding of molar mass allows chemists to scale reactions for any amount of reactant or product, facilitating the design and execution of experiments.