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Chemistry
Consider the following mathematical expressions:
a. The concentration of H+ ions is equal to the initial concentration of the acid.
b. The concentration of H+ ions is proportional to the square root of the product of the dissociation constant and the initial concentration of the acid.
c. The concentration of OH- ions is equal to twice the initial concentration of the base.
d. The concentration of OH- ions is proportional to the square root of the product of the dissociation constant and the initial concentration of the base.
For each expression, provide three scenarios where the mathematical expression would give a good approximation for the concentration of H+ or OH- ions. The initial concentrations of the acid or base are represented by [HA]0 and [B]0, respectively.
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Step 1/13
For expression a, where the concentration of H+ ions is equal to the initial concentration of the acid, this approximation holds true in the following scenarios:
Step 2/13
  1. When the acid is a strong acid that completely dissociates in water, such as hydrochloric acid or sulfuric acid.
    Step 3/13
  2. When the initial concentration of the acid is much greater than the dissociation constant, resulting in almost complete dissociation of the acid.
    Step 4/13
  3. When the concentration of any other species in the solution that could affect the concentration of H+ ions is negligible compared to the initial concentration of the acid.
For expression b, where the concentration of H+ ions is proportional to the square root of the product of the dissociation constant and the initial concentration of the acid, this approximation holds true in the following scenarios:
Step 5/13
  1. When the acid is a weak acid that does not completely dissociate in water, such as acetic acid or carbonic acid.
    Step 6/13
  2. When the initial concentration of the acid is much smaller than the dissociation constant, resulting in partial dissociation of the acid.
    Step 7/13
  3. When the concentration of any other species in the solution that could affect the concentration of H+ ions is negligible compared to the initial concentration of the acid.
For expression c, where the concentration of OH- ions is equal to twice the initial concentration of the base, this approximation holds true in the following scenarios:
Step 8/13
  1. When the base is a strong base that completely dissociates in water, such as sodium hydroxide or potassium hydroxide.
    Step 9/13
  2. When the initial concentration of the base is much greater than the dissociation constant, resulting in almost complete dissociation of the base.
    Step 10/13
  3. When the concentration of any other species in the solution that could affect the concentration of OH- ions is negligible compared to the initial concentration of the base.
For expression d, where the concentration of OH- ions is proportional to the square root of the product of the dissociation constant and the initial concentration of the base, this approximation holds true in the following scenarios:
Step 11/13
  1. When the base is a weak base that does not completely dissociate in water, such as ammonia or methylamine.
    Step 12/13
  2. When the initial concentration of the base is much smaller than the dissociation constant, resulting in partial dissociation of the base.
    Step 13/13
  3. When the concentration of any other species in the solution that could affect the concentration of OH- ions is negligible compared to the initial concentration of the base.
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