Problem 42 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Igniting \(\mathrm{MnO}_{2}\) converts it quantitatively to \(\mathrm{Mn}_{3} \mathrm{O}_{4}\). A sample of pyrolusite is of the following composition: \(\mathrm{MnO}_{2} 80 \%, \mathrm{SiO}_{2}\) andother inert constituents \(15 \%\), rest being water. The sample is ignited in air to constant weight. What is the percentage of \(\mathrm{Mn}\) in the ignited sample? \([1978]\) \([\mathrm{O}=16, \mathrm{Mn}=54.9]\)

Step-by-Step Solution

Answer

The percentage of Mn in the ignited sample is approximately 72.05%.

Step 1: Calculate Moles of Mn in MnO2

The given sample contains 80% \(\mathrm{MnO}_2\). Calculate the moles of \(\mathrm{Mn}\) based on this composition.The molar mass of \(\mathrm{MnO}_{2}\) is \(54.9 + 2 \times 16 = 86.9\) g/mol.If the sample weight is \(100\, \text{g}\), the weight of \(\mathrm{MnO}_{2}\) is \(80\, \text{g}\). Thus, the moles of \(\mathrm{MnO}_{2}\) are \(\frac{80}{86.9}\). Since each mole of \(\mathrm{MnO}_2\) contains one mole of Mn, we have the same number of moles of Mn.

Step 2: Determine Moles of Mn3O4 Formed

When \(\mathrm{MnO}_{2}\) is ignited, it forms \(\mathrm{Mn}_{3}\mathrm{O}_{4}\). The reaction is:\[ 3\ \mathrm{MnO}_2 \rightarrow \mathrm{Mn}_3\mathrm{O}_4 + \mathrm{O}_2 \]From this, 3 moles of \(\mathrm{MnO}_2\) form 1 mole of \(\mathrm{Mn}_3\mathrm{O}_4\). Thus, we calculate the moles of \(\mathrm{Mn}_3\mathrm{O}_4\) using the previously calculated moles of \(\mathrm{MnO}_2\). Let \(n\) be the moles of \(\mathrm{MnO}_2\) calculated in Step 1; then the moles of \(\mathrm{Mn}_3\mathrm{O}_4\) formed are \(\frac{n}{3}\).

Step 3: Calculate Moles of Mn in Mn3O4

\(\mathrm{Mn}_{3}\mathrm{O}_{4}\) contains three moles of Mn per mole of \(\mathrm{Mn}_{3}\mathrm{O}_{4}\) molecule. Therefore, using the moles of \(\mathrm{Mn}_3\mathrm{O}_4\) from Step 2, the moles of Mn in \(\mathrm{Mn}_3\mathrm{O}_4\) are \(3 \times \frac{n}{3} = n\).

Step 4: Calculate the Weight of Mn in the Ignited Sample

Now, calculate the total weight of Mn present in \(\mathrm{Mn}_{3}\mathrm{O}_{4}\).The atomic weight of Mn is 54.9, hence the weight of Mn due to n moles is \(n \times 54.9\). Remember \(n\) was calculated based on an 80 g portion of the 100 g sample from Step 1: \(n = \frac{80}{86.9}\). Substitute this in to find the weight of Mn.

Step 5: Determine the Total Weight of Ignited Sample

The total weight of the ignited sample is equivalent to the weight of \(\mathrm{Mn}_3\mathrm{O}_4\) since water and gaseous oxygen are lost.The formula weight of \(\mathrm{Mn}_3\mathrm{O}_4\) is \(3 \times 54.9 + 4 \times 16 = 228.7\) g/mol.Multiply the moles of \(\mathrm{Mn}_3\mathrm{O}_4\) (\(\frac{n}{3}\)) by 228.7 to obtain the weight of the ignited product.

Step 6: Calculate Percentage of Mn in Ignited Sample

Determine the percentage of Mn in the ignited sample using the weights from Step 4 and Step 5.The percentage is given by:\[\text{Percentage of Mn} = \left( \frac{\text{Weight of Mn (from Step 4)}}{\text{Weight of ignited product (from Step 5)}} \right) \times 100\%\]

Step 7: Final Step: Calculate and Present Final Result

Substitute in the equation:- From Step 4, the weight of Mn is \(\frac{80}{86.9} \times 54.9\)- From Step 5, the weight of ignited product is \(\frac{80}{86.9} \times 228.7 / 3\)Thus, the percentage is:\[\text{Percentage of Mn} = \left( \frac{\frac{80}{86.9} \times 54.9}{\frac{80}{86.9} \times 228.7 / 3} \right) \times 100\%\]Simplifying calculates approximately 72.05%.

Key Concepts

Pyrolusite

Pyrolusite is a naturally occurring mineral composed primarily of manganese dioxide ( MnO_2 ). It is commonly found in shallow oceanic deposits or in soils that have been exposed to tropical climates. The mineral is the most important ore of manganese and is inherently valuable for its use in various industrial applications, particularly in steel production.
As it forms in nature, pyrolusite can often contain impurities such as silica ( SiO_2 ) as well as other inert constituents. The typical appearance is a black or steel-grey color with a metallic luster. Understanding its composition is key in determining its reactivity during chemical processes, such as the ignition in air to form different manganese oxides.
In the exercise provided, pyrolusite undergoes a conversion process when ignited. This process is crucial in determining the percentage composition of manganese in the sample, demonstrating the practical importance of pyrolusite in industrial chemistry and stoichiometric calculations.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the relative quantities of reactants and products in chemical reactions. It uses the principles of conservation of mass to analyze chemical formulas and equations to predict the outcomes of chemical reactions.

• Stoichiometry is based on balanced chemical equations, which ensure that the mass and number of atoms are conserved during a reaction.
• This concept fundamentally relies on mole ratios derived from the coefficients of a balanced equation, which allow chemists to calculate the amounts of reactants consumed and products formed.
• The calculations often involve using molar masses to convert between mass and moles for precise measurement and analysis.

The exercise you're tackling heavily involves stoichiometry as the process of igniting pyrolusite leads to its transition from MnO_2 to Mn_3 O_4 . Understanding and calculating the moles of each substance involved help in determining the percentage of manganese present post-reaction. The practice is essential for fields like industrial chemistry where specific product characteristics like purity are necessary for successful application.

Chemical Reactions

Chemical reactions are the processes by which substances interact to form new products through the breaking and forming of chemical bonds. These transformations are often accompanied by observable changes such as evolution of gas, change in color, or temperature shifts.
Reactions are classified into several types, including synthesis, decomposition, single replacement, and double replacement among others. In this specific instance, the primary focus is on the decomposition and combination reactions that occur when pyrolusite is ignited.

• Upon heating, MnO_2 undergoes a decomposition reaction to form Mn_3 O_4 and release oxygen.
• This conversion is important in purifying manganese for further use or analysis.

Recognizing the type of reaction involved not only helps in predicting the outcome but also in calculating the resulting composition of reactants and products—which in this case, provides insight into the percentage manganese in the final product. Engaging with these reactions assists in understanding the broad applications of manganese oxides in both environmental and industrial processes.