Calculus: Equilibrium and Rate of Change
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Questions and Answers

What is the condition for stable equilibrium in the given equation?

  • d2U/dx2 = 0
  • d2U/dx2 > 0 (correct)
  • dU/dx = 0
  • d2U/dx2 < 0
  • What is the rate of change of momentum of the photons in the context of complete absorption?

  • Intensity of the wave / speed of light (correct)
  • Intensity of the wave - speed of light
  • Intensity of the wave * speed of light
  • Intensity of the wave + speed of light
  • Which reaction mechanism is responsible for the formation of Anthraquinone?

  • E2 reaction
  • Diel's alder reaction (correct)
  • Electrocyclic reaction
  • E1 reaction
  • What is the type of adsorption that releases heat and increases the electrons in π2p orbitals?

    <p>Chemisorption</p> Signup and view all the answers

    Which of the following reactions produces N2?

    <p>Both B and D</p> Signup and view all the answers

    What is the product of the Diel's alder reaction?

    <p>Anthraquinone</p> Signup and view all the answers

    What is the oxidation state of iodine in the reactant side of the given equation?

    <p>–1</p> Signup and view all the answers

    In the reaction between I⁻ and ClO₃⁻, which of the following is true?

    <p>Iodine is oxidized</p> Signup and view all the answers

    Which of the following compounds undergoes reversible hydration in aqueous solution?

    <p>R₂C=O</p> Signup and view all the answers

    What is the effect of temperature on the equilibrium of the hydration reaction?

    <p>The equilibrium is shifted towards the product at higher temperatures</p> Signup and view all the answers

    Which of the following is a correct statement about the basic strength of the given amines?

    <p>p-MeC₆H₄NH₂ is a stronger base than C₆H₅NH₂</p> Signup and view all the answers

    Which of the following compounds has the highest basic strength?

    <p>o-MeC₆H₄NH₂</p> Signup and view all the answers

    What is the correct order of basic strength of the given amines?

    <p>C₄H₅N &lt; C₅H₅N &lt; C₆H₅NH₂ &lt; o-MeC₆H₄NH₂</p> Signup and view all the answers

    Which of the following reactions is an example of acid-base reaction?

    <p>HSO₄⁻ → H₂O + SO₄²⁻</p> Signup and view all the answers

    What is the force exerted by the 21 N force on the 6 kg block?

    <p>21 N</p> Signup and view all the answers

    What is the potential energy of the particle at x = 2?

    <p>16</p> Signup and view all the answers

    What is the stable equilibrium state of the particle?

    <p>x = 3</p> Signup and view all the answers

    What is the force exerted by the light beam on the surface?

    <p>10^(-6) N</p> Signup and view all the answers

    What is the wavelength of the monochromatic light?

    <p>500 nm</p> Signup and view all the answers

    What is the power of the monochromatic light beam?

    <p>100 W</p> Signup and view all the answers

    What is the value of n in the problem?

    <p>10^(-6)</p> Signup and view all the answers

    What is the type of reaction that gives Anthraquinone as a major product?

    <p>Organic synthesis</p> Signup and view all the answers

    Study Notes

    Equilibrium and Potential Energy

    • Stable equilibrium occurs when U is minimum.
    • At stable equilibrium, d²U/dx² > 0.
    • For a particle moving along the x-axis, the potential energy is given by U = (1/3)x³ - 9x² + 20x.

    Force and Momentum

    • The force exerted by a light beam on a surface is given by F = I / c, where I is the intensity of the wave and c is the speed of light.
    • The rate of change of momentum of photons is given by dP/dt = F.

    Chemistry

    • The reaction between I⁻, ClO₃⁻, and H₂SO₄ yields Cl⁻, HSO₄⁻, and I₂.
    • Stoichiometric coefficient of HSO₄⁻ is 6 in the balanced equation.
    • Iodide is oxidized in the reaction.
    • Sulphur is reduced in the reaction.
    • H₂O is one of the products in the reaction.
    • Anthraquinone can be produced through EAS, oxidation, and Diel's Alder reaction.

    Carbonyl Compounds

    • Carbonyl compounds undergo reversible hydration in aqueous solution.
    • The equilibrium is shifted towards the product at 25°C for certain carbonyl compounds.

    Basic Strength

    • The basic strength of different amines depends on their molecular structure.
    • The correct order of basic strength varies depending on the specific amines being compared.

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    Solve calculus problems involving equilibrium and rate of change. Practice finding minimum values and determining points of equilibrium.

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