Problem 139 - A Complete Resource Book in Chemistry for JEE Main

Question

The decomposition of a certain mass of \(\mathrm{CaCO}_{3}\) gave \(11.2 \mathrm{dm}^{3}\) of \(\mathrm{CO}_{2}\) gas at STP. The mass of KOH required to completely neutralize the gas is (a) \(56 \mathrm{~g}\) (b) \(28 \mathrm{~g}\) (c) \(42 \mathrm{~g}\) (d) \(20 \mathrm{~g}\)

Step-by-Step Solution

Answer

The mass of KOH required is 56 g.

Step 1: Determine Moles of Carbon Dioxide

At standard temperature and pressure (STP), 1 mole of any gas occupies 22.4 dm³. Given that the volume of \(\mathrm{CO}_2\) produced is 11.2 dm³, use this relationship to find the moles of \(\mathrm{CO}_2\):\[\text{Moles of } \mathrm{CO}_2 = \frac{11.2 \text{ dm}^3}{22.4 \text{ dm}^3/\text{mole}} = 0.5 \text{ moles of } \mathrm{CO}_2.\]

Step 2: Neutralization Reaction

The neutralization reaction between carbon dioxide and potassium hydroxide is as follows: \[\mathrm{CO}_2 + 2\mathrm{KOH} \rightarrow \mathrm{K}_2\mathrm{CO}_3 + \mathrm{H}_2\mathrm{O}.\] According to the equation, 1 mole of \(\mathrm{CO}_2\) reacts with 2 moles of \(\mathrm{KOH}\).

Step 3: Calculate Moles of KOH Needed

Since there are 0.5 moles of \(\mathrm{CO}_2\), and the stoichiometry of the reaction requires 2 moles of \(\mathrm{KOH}\) per mole of \(\mathrm{CO}_2\), calculate the moles of \(\mathrm{KOH}\) needed: \[\text{Moles of } \mathrm{KOH} = 0.5 \times 2 = 1 \text{ mole of } \mathrm{KOH}.\]

Step 4: Calculate Mass of KOH Required

Using the molar mass of potassium hydroxide (\(\mathrm{KOH}\)), which is approximately 56 g/mol, calculate the mass required: \[\text{Mass of } \mathrm{KOH} = 1 \text{ mole} \times 56 \text{ g/mol} = 56 \text{ g}.\]

Key Concepts

Stoichiometry

In chemical reactions, stoichiometry helps us understand the relationship between reactants and products. This concept uses balanced chemical equations to determine the proportions in which these chemicals react.
Through stoichiometry, you can calculate the amount of each substance needed or produced in a reaction. In the original exercise, stoichiometry is essential—it tells us that one mole of carbon dioxide reacts with two moles of potassium hydroxide (KOH), which is crucial to solving the problem. As we know the number of moles of carbon dioxide, we use stoichiometry to find the corresponding moles of KOH required for neutralization.

Gas Laws

Gas laws, such as Avogadro's Law and Boyle's Law, describe how gases behave under different conditions of pressure, temperature, and volume. These principles help us determine the volume occupied by a gas at standard conditions.
According to Avogadro's Law, at STP, one mole of any gas occupies 22.4 liters (or dm³). This knowledge allows us to find the moles of carbon dioxide based on its given volume. In our exercise, by using the relation that 1 mole = 22.4 dm³, we calculated the moles of \(\mathrm{CO}_2\). This conversion is fundamental to proceed with calculations for the neutralization process.

Neutralization Reaction

A neutralization reaction involves an acid-base reaction where an acid and a base produce salt and water. For the exercise, carbon dioxide, a weak acid, reacts with potassium hydroxide, a strong base.
Consider the equation given: \[\mathrm{CO}_2 + 2\mathrm{KOH} \rightarrow \mathrm{K}_2\mathrm{CO}_3 + \mathrm{H}_2\mathrm{O}.\]
This balanced equation shows that each mole of carbon dioxide reacts with two moles of potassium hydroxide, resulting in the formation of potassium carbonate and water. Recognizing this relationship is critical to determine the amount of KOH needed to neutralize a given amount of carbon dioxide.

Molar Mass

Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol). It is derived from the atomic masses of the elements in a compound.
For example, to calculate molar mass of potassium hydroxide (KOH), you add together the atomic masses: potassium (K) approximately 39 g/mol, oxygen (O) 16 g/mol, and hydrogen (H) 1 g/mol. The molar mass of KOH is approximately 56 g/mol.
This means one mole of potassium hydroxide weighs 56 grams, and this knowledge is key to converting moles into measurable mass for practical uses, like the amount needed in the neutralization reaction.

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) are conditions often used in chemistry to make experiments and calculations more standardized. STP is defined as a temperature of 273.15 K (0 °C) and a pressure of 1 atm (101.3 kPa).
Under these conditions, gases have predictable properties, like occupying 22.4 liters per mole, as mentioned earlier.
Knowing that the reaction occurs at STP tells us we can trust these calculations of volume to moles conversion, and use it to determine how much reactive material is needed in the given scenario.