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The conductivities at infinite solution of NH4Cl, NaOH and NaCl are 130,218,120ohm1cm2eq1. If equivalent conductance of N1000 solution of NH4OH is 10ohm1cm2eq1, then degree of dissociation of NH4OH at this dilution is:
A.0.005
B.0.043
C.0.01
D.0.02

Answer
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Hint: We can say equivalent conductivity as the conducting power of all the ions produced by dissolving one gram equivalent of an electrolyte present in solution. We can calculate the degree of dissociation using m and m(NH4OH). We can calculate the m(NH4OH) using the values of m(NH4Cl), m(NaOH) and m(NaCl).

Complete step by step answer:
Given data contains,
The conductivity of NH4Cl is 130ohm1cm2eq1.
The conductivity of NaOH is 218ohm1cm2eq1.
The conductivity of NaCl is 210ohm1cm2eq1.
The reaction of ammonium chloride with sodium hydroxide results in the formation of ammonium hydroxide and sodium chloride. We can write the chemical equation as,
NH4OH+NaClNaCl+NH4OH
At infinite dilution, the conductivity of NH4OH is,
NH4OH=NH4++OH
Now,
m(NH4OH)=m(NH4Cl)+m(NaOH)m(NaCl)
The equivalent conductance of NH4OH is calculated by adding the conductivities of NH4Cl, NaOH and subtracting the obtained conductivity with conductivity of NaCl.
Let us now substitute the values the conductivities of NH4Cl, NaOH and NaCl to get m(NH4OH).
m(NH4OH)=m(NH4Cl)+m(NaOH)m(NaCl)
m(NH4OH)=130+218120
m(NH4OH)=228
The value of m(NH4OH) is 228.
The equivalence conduction of solution of N100NH4OH is 10ohm1cm2eq1.
Equivalent conductance (m) is 10ohm1cm2eq1.
We can calculate the degree of dissociation with m and m. The formula to calculate the degree of dissociation is given as,
α=mm
Here, α represents the degree of dissociation of NH4OH.
Equivalent conductance (m) is 10ohm1cm2eq1.
The value of m(NH4OH) is 228.
Using the values of mand m, we can calculate the degree of dissociation as,
α=mm
α=10228
α=0.043
The degree of dissociation of NH4OH is 0.043.
Therefore, the option (B) is correct.

Note: We can say that conductivity (or) specific conductivity is the capacity of solution to conduct electricity. We can represent the SI unit of conductivity as S/m. The unit that is used to express molar conductivity is Sm2mol1. We can obtain the limiting molar conductivity of any electrolytes with the help of Kohlraush’s law.