Problem 31 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The ammonia prepared by treating ammonium sulphate with calcium hydroxide is completely used by \(\mathrm{NiCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) to form a stable coordination compound. Assume that both the reactions are \(100 \%\) complete. If \(1584 \mathrm{~g}\) of ammonium sulphate and \(952 \mathrm{~g}\) of \(\mathrm{NiCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) are used in the preparation, the combined weight (in grams) of gypsum and the nickel-ammonia coordination compound thus produced is(Atomic weights in \(\mathrm{g} \mathrm{mol}^{-1}\) : \(\mathrm{H}=1, \mathrm{~N}=14, \mathrm{O}=16, \mathrm{~S}=32, \mathrm{Cl}=35.5, \mathrm{Ca}=\) \(40, \mathrm{Ni}=59\) )

Step-by-Step Solution

Answer

The combined weight is 2556 grams.

Step 1: Calculate Moles of Ammonium Sulphate

First, find the molar mass of \((NH_4)_2SO_4\). With atomic weights given, we have: \(2(14 + 4) + 32 + 4(16) = 132\,\text{g/mol}\).Now, calculate the moles of \((NH_4)_2SO_4\):\[\text{Moles of } (NH_4)_2SO_4 = \frac{1584\, \text{g}}{132\,\text{g/mol}} = 12\, \text{moles}\].

Step 2: Determine Moles of Calcium Hydroxide Required

The reaction between ammonium sulfate and calcium hydroxide is:\((NH_4)_2SO_4 + Ca(OH)_2 \rightarrow CaSO_4 + 2NH_3 + 2H_2O\).Thus, for every 1 mole of ammonium sulfate, 1 mole of calcium hydroxide is required. Therefore, 12 moles of calcium hydroxide are needed.

Step 3: Calculate Moles of Nickel(II) Chloride Hexahydrate

Find the molar mass of \(NiCl_2 \cdot 6H_2O\): \(59 + 2(35.5) + 6(18) = 237\,\text{g/mol}\).Calculate the moles of \(NiCl_2 \cdot 6H_2O\):\[\text{Moles of } NiCl_2 \cdot 6H_2O = \frac{952\, \text{g}}{237\,\text{g/mol}} = 4\, \text{moles}\].

Step 4: Establish Reaction Stoichiometry of Nickel-Ammonia Coordination

Given the reaction,\[NiCl_2 \cdot 6H_2O + 6NH_3 \rightarrow [Ni(NH_3)_6]Cl_2 + 6H_2O\].4 moles of \(NiCl_2 \cdot 6H_2O\) will react with 24 moles of ammonia.Since 12 moles of \((NH_4)_2SO_4\) produce 24 moles of \(NH_3\), the reaction is complete.

Step 5: Calculate Molar Mass of Calcium Sulfate

For \(CaSO_4\), the molar mass is: \(40 + 32 + 4(16) = 136\,\text{g/mol}\).

Step 6: Calculate Molar Mass of the Nickel-Ammonia Compound

For \([Ni(NH_3)_6]Cl_2\), calculate the molar mass:\(59 + 6(17) + 2(35.5) = 231\,\text{g/mol}\).

Step 7: Compute Mass of Products Formed

Calculate the mass of gypsum, using moles of \((NH_4)_2SO_4\):\[12\,\text{moles} \times 136\,\text{g/mol} = 1632\,\text{g}\].For \([Ni(NH_3)_6]Cl_2\), using moles of \(NiCl_2 \cdot 6H_2O\):\[4\,\text{moles} \times 231\,\text{g/mol} = 924\,\text{g}\].

Step 8: Add Masses of Products

Combine the masses:\[1632\,\text{g} + 924\,\text{g} = 2556\,\text{g}\].

Key Concepts

Molar Mass Calculation

Calculating molar mass is a fundamental skill in chemistry that helps us understand the composition of molecules and compounds. Molar mass refers to the mass of one mole of a substance. It is expressed in grams per mole (g/mol). To calculate it, you must add the atomic masses of all the atoms in a molecule.
For example, to calculate the molar mass of ammonium sulfate \((NH_4)_2SO_4\), follow these steps:

• Identify the atoms: Nitrogen (N), Hydrogen (H), Sulfur (S), and Oxygen (O).
• Multiply by the subscript: 2 Nitrogens, 8 Hydrogens, 1 Sulfur, and 4 Oxygens.
• Add their atomic masses: 2(14) + 8(1) + 32 + 4(16) = 132 g/mol.

This concept is crucial because it leads to determining other properties, like the number of moles, which is necessary for chemical reactions and stoichiometry.

Stoichiometry

Stoichiometry is the calculation of reactants and products in a chemical reaction. It helps predict how much product is formed from a given amount of reactants, making it a pivotal concept in chemistry. At its core, stoichiometry uses balanced chemical equations and the principle of conservation of mass.
To understand stoichiometry, consider the reaction of ammonium sulfate and calcium hydroxide to produce ammonia:

• Balanced Equation: \((NH_4)_2SO_4 + Ca(OH)_2 \rightarrow CaSO_4 + 2NH_3 + 2H_2O\)
• Use the reaction to determine mole ratios: 1:1 for ammonium sulfate to calcium hydroxide, 1:2 for ammonium sulfate to ammonia.
• Calculate how many moles of product are produced: 12 moles of ammonium sulfate yield 24 moles of ammonia and 12 moles of calcium sulfate (gypsum).

Stoichiometry is indicative of how mathematical calculations can efficiently predict the outcome of chemical reactions.

Chemical Reactions

Chemical reactions describe the process where reactants transform into products. They are depicted through chemical equations, which must be balanced to comply with the conservation of mass. Every reaction involves breaking and forming chemical bonds.
In this exercise, consider two key reactions:

• Ammonium sulfate reacts with calcium hydroxide, creating gypsum \((CaSO_4)\), water, and ammonia.
• Ammonia further reacts with nickel(II) chloride hexahydrate to create a coordination compound \[Ni(NH_3)_6]Cl_2\].

Chemical reactions are guided by molecular collusions, energy changes, and reaction conditions like temperature and concentration. Understanding how molecules interact in these processes is essential to mastering more complex chemistry topics.