**Balancing Chemical Equations Using Vector Approach****Question 11:**The following reaction between potassium permanganate and manganese sulfate in water produces manganese dioxide, potassium sulfate, and sulfuric acid:\[(x_1)KMnO_4 + (x_2)MnSO_4 + (x_3)H_2O \rightarrow (x_4)MnO_2 + (x_5)K_2SO_4 + (x_6)H_2SO_4\]**Instructions:**Balance the above chemical equation using the vector approach, and write the solution in vector parametric form.**Explanation of Vector Approach:**The vector approach involves expressing the balancing of the chemical equation in the form of vectors, which represent the coefficients of each compound in the reaction. The goal is to adjust these coefficients so that the number of atoms of each element is the same on both sides of the equation.1. **Identify the Elements:** In this equation, the elements involved are Potassium (K), Manganese (Mn), Oxygen (O), Sulfur (S), and Hydrogen (H).2. **Set Up the System of Equations:** Based on the individual elements, write the equations needed to balance the number of atoms of each element.3. **Matrix Representation:** Represent the system of equations as a matrix to be solved. Each row corresponds to the coefficients of a particular element.4. **Solve the Matrix:** Use linear algebra techniques to find the balanced coefficients (values of \(x_1, x_2, x_3, x_4, x_5\), and \(x_6\)).By following this systematic procedure, you will determine the balanced chemical equation ensuring that there are equal numbers of each type of atom on both sides of the equation.**Note for Students:**While solving using vectors can seem complex at first, it offers a clear and organized method for ensuring the reaction is accurately balanced, particularly for more complicated reactions. This technique is especially valuable in higher-level chemistry coursework.**Additional Resources:**- Lectures on balancing chemical equations- Practice problems for vector approach balancing- Tutorials on matrix operations in the context of chemical equationsUnderstanding this method deeply equips you with a powerful toolset for tackling various chemical reactions in both academic and real-world scenarios.

To balance the equation using the vector approach, we assign variables (coefficients) to the…

1. The following reaction between potassium, permanganate, and manganese sulfate in water produces maga- nese dioxide, potassium sulfate, and sulfuric acid. (1₁) KMnO4 + (x₂)MnSO4 + (13)H₂O → (14) MnO₂ + (15) K₂SO4 + (16) H₂SO4 Balance the equation using the vector approach and write the solution in vector parametric form.

1. The following reaction between potassium, permanganate, and manganese sulfate in water produces maga- nese dioxide, potassium sulfate, and sulfuric acid. (1₁) KMnO4 + (x₂)MnSO4 + (13)H₂O → (14) MnO₂ + (15) K₂SO4 + (16) H₂SO4 Balance the equation using the vector approach and write the solution in vector parametric form.

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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