Calculus: Equilibrium and Rate of Change

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22 Questions

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

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

Which reaction mechanism is responsible for the formation of Anthraquinone?

Diel's alder reaction

What is the type of adsorption that releases heat and increases the electrons in π2p orbitals?

Chemisorption

Which of the following reactions produces N2?

Both B and D

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

Anthraquinone

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

–1

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

Iodine is oxidized

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

R₂C=O

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

The equilibrium is shifted towards the product at higher temperatures

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

p-MeC₆H₄NH₂ is a stronger base than C₆H₅NH₂

Which of the following compounds has the highest basic strength?

o-MeC₆H₄NH₂

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

C₄H₅N < C₅H₅N < C₆H₅NH₂ < o-MeC₆H₄NH₂

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

HSO₄⁻ → H₂O + SO₄²⁻

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

21 N

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

16

What is the stable equilibrium state of the particle?

x = 3

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

10^(-6) N

What is the wavelength of the monochromatic light?

500 nm

What is the power of the monochromatic light beam?

100 W

What is the value of n in the problem?

10^(-6)

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

Organic synthesis

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.

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

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