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At 180C the mobilities of NH+4 and ClO-4 ions are 6.6 x 10-4 and 5.7 x 10-4 cm2 volt-1s-1 at infinite dilution. The value of equivalent conductance of ammonium perchlorate solution at infinite dilution
  • a)
    1.187 x 10-2Sm2eq-1
  • b)
    2.284 x 10-3 Sm2eq-1
  • c)
    1.87 x 10-5Sm2eq-1
  • d)
    2.09 x 10-6 Sm2eq-1
Correct answer is option 'A'. Can you explain this answer?
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At 180C the mobilities of NH+4 and ClO-4 ions are 6.6 x 10-4 and 5.7 x...

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At 180C the mobilities of NH+4 and ClO-4 ions are 6.6 x 10-4 and 5.7 x...
Given:
- Temperature (T) = 180°C = 453 K
- Mobilities of NH4+ and ClO4- ions at infinite dilution:
- μ(NH4+) = 6.6 x 10^-4 cm^2 V^-1 s^-1
- μ(ClO4-) = 5.7 x 10^-4 cm^2 V^-1 s^-1

To find:
The value of equivalent conductance of ammonium perchlorate (NH4ClO4) solution at infinite dilution.

Explanation:

Step 1: Convert the temperature to Kelvin:
T = 180°C = 453 K

Step 2: Calculate the equivalent conductance (Λ) of NH4+ and ClO4- ions:
The equivalent conductance (Λ) of an ion is given by the equation:

Λ = κ / c
where κ is the specific conductance and c is the concentration of the ion.

At infinite dilution, the specific conductance (κ) is equal to the mobility (μ) multiplied by the molar conductivity at infinite dilution (Λ0):

κ = μ * Λ0

Since we are given the mobilities of NH4+ and ClO4- ions at infinite dilution, we can calculate their equivalent conductances:

Λ(NH4+) = μ(NH4+) * Λ0(NH4+)
Λ(ClO4-) = μ(ClO4-) * Λ0(ClO4-)

Step 3: Calculate the molar conductivity at infinite dilution (Λ0):
The molar conductivity at infinite dilution (Λ0) can be calculated using the Kohlrausch's law of independent migration of ions:

Λ0 = Λ - A * √c

where Λ is the equivalent conductance at a given concentration, A is a constant, and c is the concentration.

At infinite dilution, the concentration (c) approaches zero, so the term A * √c becomes negligible.

Therefore, Λ0 = Λ

Step 4: Calculate the equivalent conductance of the ammonium perchlorate (NH4ClO4) solution:
The equivalent conductance of the ammonium perchlorate (NH4ClO4) solution at infinite dilution can be calculated by adding the equivalent conductances of the NH4+ and ClO4- ions:

Λ(NH4ClO4) = Λ(NH4+) + Λ(ClO4-)

Substituting the values of μ(NH4+), μ(ClO4-), and Λ0 into the equations, we get:

Λ(NH4+) = 6.6 x 10^-4 cm^2 V^-1 s^-1 * Λ0(NH4+)
Λ(ClO4-) = 5.7 x 10^-4 cm^2 V^-1 s^-1 * Λ0(ClO4-)

Λ(NH4ClO4) = Λ(NH4+) + Λ(ClO4-)

Step 5: Calculate the value of Λ0(NH4+) and Λ0(Cl
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At 180C the mobilities of NH+4 and ClO-4 ions are 6.6 x 10-4 and 5.7 x 10-4 cm2 volt-1s-1 at infinite dilution. The value of equivalent conductance of ammonium perchlorate solution at infinite dilutiona)1.187 x 10-2Sm2eq-1b)2.284 x 10-3 Sm2eq-1c)1.87 x 10-5Sm2eq-1d)2.09 x 10-6 Sm2eq-1Correct answer is option 'A'. Can you explain this answer?
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