91影视

Nanotechnology has become an important field, with applications ranging from high-density data storage to the design of 鈥渘ano machines.鈥� One common building block of nano structured architectures is manganese oxide nano particles. The particles can be formed from manganese oxalate nano rods, the formation of which can be described as follows: $$\mathrm{Mn}^{2+}(a q)+\mathrm{C}_{2} \mathrm{O}_{4}^{2-}(a q) \rightleftharpoons \mathrm{MnC}, \mathrm{O}_{4}(a q) \quad K_{1}=7.9 \times 10^{3}$$ $$\mathrm{MnC}_{2} \mathrm{O}_{4}(a q)+\mathrm{C}_{2} \mathrm{O}_{4}^{2-}(a q) \rightleftharpoons \mathrm{Mn}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{2}^{2-}(a q) \quad K_{2}=7.9 \times 10^{1}$$ Calculate the value for the overall formation constant for \(\mathrm{Mn}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{2}^{2-} :\) $$K=\frac{\left[\mathrm{Mn}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{2}^{2-}\right]}{\left[\mathrm{Mn}^{2+}\right]\left[\mathrm{C}_{2} \mathrm{O}_{4}^{2-}\right]^{2}}$$

Step by step solution

01

Write down the first equilibrium reaction and its constant

Mn虏鈦�(aq) + C鈧侽鈧劼测伝(aq) 鉄� MnC鈧侽鈧�(aq), K鈧� = 7.9 脳 10鲁 Step 2: Reaction 2

02

Write down the second equilibrium reaction and its constant

MnC鈧侽鈧�(aq) + C鈧侽鈧劼测伝(aq) 鉄� Mn(C鈧侽鈧�)鈧偮测伝(aq), K鈧� = 7.9 脳 10鹿 Step 3: Overall Formation Reaction

03

Determine the overall reaction for the formation of Mn(C鈧侽鈧�)鈧偮测伝

To obtain the overall formation reaction, we add Reaction 1 and Reaction 2: Mn虏鈦�(aq) + 2 C鈧侽鈧劼测伝(aq) 鉄� Mn(C鈧侽鈧�)鈧偮测伝(aq) Step 4: Calculate the Overall Formation Constant

04

Use the given equilibrium constants to find the overall formation constant, K

The overall formation constant K is the product of K鈧� and K鈧�: K = K鈧� 脳 K鈧� = (7.9 脳 10鲁) 脳 (7.9 脳 10鹿) K = 62.41 脳 10鈦� K = 6.24 脳 10鈦� The overall formation constant for the species Mn(C鈧侽鈧�)鈧偮测伝 is approximately 6.24 脳 10鈦�.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Manganese Oxide Nanoparticles

Manganese oxide nanoparticles ( Mo_n Ps) are a type of nanomaterial made up of manganese and oxygen that have inspired numerous scientific investigations due to their unique properties. These nanoparticles are particularly interesting because they have a high surface area to volume ratio, which influences their physical and chemical behaviors. This characteristic makes them suitable for use in various applications:

• They are used as catalysts in chemical reactions, helping to speed up the rate of reaction without being consumed.
• Their magnetic properties make them ideal in applications such as data storage, where they enable new possibilities for higher density storage options.
• They are also useful in the environmental field for remediating pollutants, as they can be tailored to absorb or catalyze the breakdown of hazardous substances.

By engineering nanoparticles with specific sizes, shapes, and compositions, researchers can optimize their performance for these and other applications. This engineering often involves forming these nanoparticles from compounds, such as manganese oxalate nanorods, as a part of the fabrication process. Understanding how these materials form helps in creating more efficient nanomaterials for various applications.

Equilibrium Constant

The equilibrium constant, denoted as \( K \), is a crucial concept in chemistry that helps predict the direction and extent of a reaction. It relates to the concentrations of the reactants and products at equilibrium in a chemical reaction. For a reversible reaction at equilibrium, such as:\[aA + bB \rightleftharpoons cC + dD\]the equilibrium constant \( K \) is expressed as:\[K = \frac{[C]^c [D]^d}{[A]^a [B]^b}\]This expression tells us the relative concentrations of products to reactants at equilibrium, allowing us to determine:

• Whether the reactants or products are favored in the equilibrium mix.
• If \( K > 1 \), the products are favored.
• If \( K < 1 \), the reactants are favored.
• When \( K \) is approximately equal to 1, significant amounts of both reactants and products are present.

In the context of manganese oxide nanoparticles, equilibrium constants help determine the efficiency and yield of nanoparticle synthesis, ensuring that the desired products are produced in optimal quantities. Calculating the overall formation constant involves multiplying individual equilibrium constants from contributing reactions, providing insight into the overall stability of a complex in solution.

Formation Reaction

A formation reaction is a process where specific compounds or elements combine to form a new compound. Understanding formation reactions is essential, especially when synthesizing materials like manganese oxide nanoparticles. The given exercise demonstrates a typical multi-step formation reaction involving manganese oxalate:

• In the first step, manganese ( Mn^{2+} ions) reacts with oxalate ions ( C_2O_4^{2-} ) to form manganese oxalate ( MnC_2O_4 ).
• The second step involves further reaction with additional oxalate ions to form Mn( C_2O_4 )_2^{2-}, a more complex ion.

Together, these steps result in the formation of a compound that eventually contributes to the formation of manganese oxide nanoparticles.
The overall formation constant is crucial for these reactions, as it helps predict the likelihood of each step. By combining reactions, we get the full picture of how a particular product is formed, and how stable it is. This stability, indicated by the equilibrium constant, influences the conditions needed for successful nanomaterial synthesis.