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How to calculate the equivalent weight of potassium carbonate?

Answer
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Hint: Equivalent weight of any particular chemical element, acid, base or salt is defined as the quantity of substance that reacts with a fixed quantity of another substance in a chemical reaction like with 1 part of hydrogen or 35.5 part of chlorine. It is a term of great significance in Stoichiometry.

Complete answer:
Equivalent weight is calculated by the formula as-Molecular weight/valency factor(n).
Valency factor is calculated differently for Acids, Bases and salts.
For element n is valency
Example-Equivalent weight of Calcium is $40/2 = 20$where 40 is mass of Calcium and 2 is the valency
For Acids n is basicity (Number of Replaceable ${H^ + }$ ions present in the acid)
Example-Equivalent weight of ${H_2}S{O_4} = 98/2 = 49$ here 98 is the molecular weight of the acid and 2 the valency factor.
For Bases n is Acidity (Number of Replaceable $O{H^ - }$ ions present in the base)
Example- Equivalent weight of $NaOH = 40/1 = 40$ here 40 is the molecular weight of the base and 1 is the valency factor.
For salts n is total positive or negative charge on the salt
Given in the question we are given Potassium Carbonate ${K_2}C{O_3}$ .It ionizes as follows-
${K_2}C{O_3} \to 2{K^ + } + C{O_3}^{2 - }$
Thus the total positive or negative charge here is 2 and thus $n = 2$
Molecular Mass of the salt is 138g
(Mass of Potassium is 39 g, Mass of Oxygen is 16 g and mass of Carbon is 12 g)
$2 \times 39 + 12 + 3 \times 16 = 138$
Hence Equivalent Mass will be $138/2 = 68g$

Note:
The concept of Equivalent weight is very important. It is used to calculate the Normality of a solution. Normality is an important concept to calculate the Concentration of the solution. It is generally given by the number of grams Equivalent present in a litre of solution. Here the number of grams Equivalent is Number of moles divided by the Equivalent weight.