Problem 64 - A Complete Resource Book in Chemistry for JEE Main

Question

What is the molarity of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) solution that has a density \(1.84 \mathrm{~g} / \mathrm{cc}\) at \(35^{\circ} \mathrm{C}\) and contains \(98 \% \mathrm{H}_{2} \mathrm{SO}_{4}\) by weight? (a) \(1.84 \mathrm{M}\) (b) \(81.4 \mathrm{M}\) (c) \(18.4 \mathrm{M}\) (d) \(184 \mathrm{M}\)

Step-by-Step Solution

Answer

The molarity of the \(\mathrm{H}_{2}\mathrm{SO}_{4}\) solution is approximately \(18.4 \mathrm{M}\). Therefore, the answer is (c) \(18.4 \mathrm{M}\).

Step 1: Understand the Problem

We need to find the molarity (M) of a sulfuric acid solution. The molarity is given by the number of moles of solute (in this case, sulfuric acid, \( \mathrm{H}_{2}\mathrm{SO}_{4} \)) per liter of solution. We have the density and weight percent of the solution.

Step 2: Determine the Mass of Solution

Start by assuming 1 cc (or 1 mL) of solution. The density of the solution is given as \(1.84 \mathrm{~g/cc}\), so the mass of 1 mL of this solution is \(1.84 \mathrm{~g}\).

Step 3: Calculate Mass of \(\mathrm{H}_{2}\mathrm{SO}_{4}\)

The solution is \(98\%\) \(\mathrm{H}_{2}\mathrm{SO}_{4}\) by weight. Therefore, the mass of \(\mathrm{H}_{2}\mathrm{SO}_{4}\) in 1 mL of solution is \(0.98 \times 1.84\) g.

Step 4: Convert Mass to Moles

Determine the molar mass of \(\mathrm{H}_{2}\mathrm{SO}_{4}\) which is approximately \(98.08 \mathrm{~g/mol}\). Use this to convert the mass of \(\mathrm{H}_{2}\mathrm{SO}_{4}\) to moles: \[ \text{moles of } \mathrm{H}_{2}\mathrm{SO}_{4} = \frac{0.98 \times 1.84}{98.08} \text{ moles} \]

Step 5: Convert Volume to Liters

Since we started with 1 mL of solution, convert this volume to liters: \[ 1 \text{ mL} = 0.001 \text{ L} \]

Step 6: Calculate Molarity

Molarity (M) is calculated as the number of moles of solute per liter of solution. Thus, \[ \text{Molarity} = \frac{\text{moles of } \mathrm{H}_{2}\mathrm{SO}_{4}}{0.001 \text{ L}} \]Substitute the value from Step 4:\[ \text{Molarity} = \frac{0.98 \times 1.84}{98.08 \times 0.001} \approx 18.4 \text{ M} \]

Step 7: Conclusion: Choose the Correct Answer

Based on the above calculation, the molarity of the solution is approximately \(18.4 \mathrm{M}\). The correct answer is therefore (c) \(18.4 \mathrm{M}\).

Key Concepts

Density

Density is a key property of a substance that tells us how much mass is contained in a given volume. In this specific exercise, the density of the sulfuric acid solution is given as 1.84 g/cc (grams per cubic centimeter), which means that each cubic centimeter (or milliliter) of the solution weighs 1.84 grams. This information is essential when we need to convert between volume and mass, which is a crucial step in finding the molarity of the solution.

Understanding density helps us relate how solutions are physically composed of molecules and how they can be quantified. For calculations, keeping track of units is important, and knowing that 1 cc is equivalent to 1 mL is helpful. This makes the conversion between different units seamless when working through chemical problems.

Weight Percent

Weight percent is a way to express the concentration of a component in a mixture. It is defined as the mass of the solute divided by the total mass of the solution, multiplied by 100 to get a percentage. In this example, we have a sulfuric acid solution that contains 98% \(H_2SO_4\) by weight. This percentage indicates that in 100 grams of solution, 98 grams are sulfuric acid, with the remaining 2 grams making up the rest of the solution.

Using weight percent is particularly useful in chemistry to describe the mixture's makeup and to further carry out mole and concentration calculations. Knowing the weight percent allows us to determine how much of the solute we have in a given portion, which is important when planning to convert this mass into moles.

Sulfuric Acid

Sulfuric acid (\(\mathrm{H}_{2}\mathrm{SO}_{4}\)) is a highly corrosive strong mineral acid with various applications, including domestic acidic drain cleaner, electrolyte in lead-acid batteries, and as a dehydrating agent. It is important to understand the role it plays in industry owing to its reactive nature and ability to alter other substances.

When calculating the properties of a sulfuric acid solution, knowing its molar mass is essential. The molar mass of sulfuric acid is approximately 98.08 g/mol. By understanding this, we are able to convert the mass of \(\mathrm{H}_{2}\mathrm{SO}_{4}\) within a solution into moles, which is a crucial step in determining its molarity.

Mole Calculations

Mole calculations form the backbone of most quantitative chemistry questions, including those involving solutions and concentrations. To find molarity, we need to convert the mass of the solute into moles, then divide by the volume in liters.

In our exercise, after calculating the mass of \(\mathrm{H}_{2}\mathrm{SO}_{4}\) present in 1 mL of solution, we use its molar mass to convert to moles. With the moles determined and knowing that 1 mL = 0.001 L, we divide the number of moles by the volume in liters to find the molarity. As a rule of thumb, always ensure the units align: grams to moles using molar mass and milliliters to liters with a straightforward conversion. This systematic approach allows for precise calculation in determining molarity.