Must Be Your Own Work Due ASAP: A Wet Cell Is Constructed

Must Be Your Own Workdue Asap1 A Wet Cell Is Constructed And

Must Be Your Own Workdue Asap1 A Wet Cell Is Constructed And

1. A wet cell is constructed and the salt bridge was replaced with a piece of copper wire. Does the cell produce a sustainable current and why or why not? The cell would not produce a sustainable current because the wire cannot balance the accumulation of charges in each of the half-cells. The salt bridge traditionally allows ions to flow between the two compartments, maintaining electrical neutrality. Replacing the salt bridge with a copper wire disrupts this process because the wire only provides a conductive path for electrons, not ions. This prevents the flow of ions necessary to neutralize charge build-up, leading to cessation of the current after a short period. Without ionic flow to counterbalance charge accumulation, the electrochemical reaction ceases, making the current unsustainable (Brown, LeMay, Bursten, Murphy, & Woodward, 2020).

2. A one-to-one function and its inverse can be used to make information secure. The function is used to encrypt a message, and its inverse is used to decrypt the encrypted message. The assignment involves using a mathematical function to encode messages. For example, the function f(x) = 3x - 1 assigns numerical values to letters, with A=1, B=2, etc. To encrypt a message like "HELLO," each letter is converted to its numeric value: H=8, E=5, L=12, L=12, O=15. Applying f(x) to the sequence gives the encrypted values: f(8)=3(8)-1=23, f(5)=3(5)-1=14, f(12)=3(12)-1=35, but since alphabet values are 1-26, the encryption would be capped or adjusted accordingly. The inverse function of f(x)=3x-1 is f⁻¹(y)=(y+1)/3. This inverse is used to decrypt, reconstructing the original message by applying the inverse function to the encrypted values (Strang, 2016). In this exercise, I created my own encryption function: g(x)=4x+2. The letter topic I chose related to our discussion on electrochemical cells. The message I encrypted was "BATTERY," which translates to numeric values B=2, A=1, T=20, T=20, E=5, R=18, Y=25. Applying g(x): for B, g(2)=4(2)+2=10; for A, g(1)=4(1)+2=6; and so on, resulting in encrypted numbers.

To decrypt, I found the inverse function of g(x)=4x+2, which is g⁻¹(y)=(y-2)/4. By applying this to the encrypted message, I recovered the original sequence of numbers and thus the word "BATTERY." This process illustrates how a one-to-one function and its inverse serve as fundamental tools in cryptography by allowing secure encoding and decoding of information, which is essential for maintaining data confidentiality in various applications, including digital communication about electrochemical systems and energy storage (Katz & Lindell, 2014).

Paper For Above instruction

Understanding the functionality of electrochemical cells requires examining the roles of components like salt bridges and conducting pathways. A wet cell relies on a salt bridge—a U-shaped tube filled with electrolyte—to facilitate the flow of ions between two half-cells, thereby maintaining electrical neutrality and enabling continuous current flow (Brown et al., 2020). When this salt bridge is replaced with a copper wire, the cell cannot sustain a current because the wire only conducts electrons, not ions. The ionic flow essential for balancing charge cannot occur, leading to a halt in the electrochemical reaction. This disruption underscores the salt bridge’s critical role in electrochemistry, facilitating ion exchange that sustains the cell’s operation.

Similarly, the use of one-to-one functions and their inverses highlights the importance of mathematical principles in securing information. Encryption functions, such as f(x)=3x-1, assign numerical values to alphabetic characters and transform them into coded messages. The inverse function, f⁻¹(y)=(y+1)/3, allows for decoding the message by reverting the encryption process. An example encryption of the word "HELLO" involves converting each letter to its numeric equivalent and applying the function, producing encrypted values that only the inverse function can decode effectively. This process illustrates the fundamental role of invertible functions in cryptography, ensuring that messages remain confidential and can be securely transmitted and recovered.

Creating personalized encryption functions—like g(x)=4x+2—and applying them to relevant class topics enhances understanding of how mathematical operations underpin digital security systems. In particular, encrypting a term such as "BATTERY" and decrypting it using the inverse function demonstrates practical application in protecting information about electrochemical cells and energy technologies. The symmetry between encryption and decryption functions emphasizes how mathematical inverse operations are vital for safeguarding data, whether in electrical technology or cybersecurity (Katz & Lindell, 2014; Strang, 2016). This connection between chemistry and cryptography exemplifies the interdisciplinary nature of science and mathematics, illustrating their combined utility in advancing secure communication and sustainable energy solutions.

References

  • Brown, T. L., LeMay, H. E., Bursten, B. E., Murphy, C., & Woodward, P. (2020). Chemistry: The central science (14th ed.). Pearson.
  • Katz, J., & Lindell, Y. (2014). Introduction to modern cryptography. Chapman and Hall/CRC.
  • Strang, G. (2016). Introduction to linear algebra (5th ed.). Wellesley-Cambridge Press.

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