# The unit of equilibrium constant for the reversible reaction H2 + I2 = 2HI, is

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The unit of equilibrium constant for the reversible reaction H2 + I2 = 2HI, is
1. mol-1 litre
2. mol-2 litre
3. mol litre-1
4. None of these

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Correct Answer - Option 4 : None of these

Concept:

• Law of Mass action and Equilibrium constant:
• At a constant temperature, the rate of a chemical reaction is directly proportional to the product of molar concentrations of reactants present at any given time. This is the law of mass action.
• The equilibrium constant for the reversible reaction of type $aA + bB \rightleftharpoons cC + dD$ is represented as

${K_{\rm{c}}}{\rm{ = }}\frac{{{{{\rm{[C]}}}^{\rm{c}}}{{{\rm{[D]}}}^{\rm{d}}}}}{{{{{\rm{[A]}}}^{\rm{a}}}{{{\rm{[B]}}}^{\rm{b}}}}}$

Characteristics of an equilibrium constant:

• It is a definite value for all chemical reactions.
• The constants Kp and Kc are both equilibrium constants.
• Kp is used when the concentration terms are given in partial pressures i.e, in gaseous reactions.
• Kc is used when the reaction terms are expressed in molarities.
• The relation between Kp and Kis given by:

${K_p} = {K_c} × {\left( {RT} \right)^{\Delta n}}$ where R = Universal gas constant, T = Temperature, and $\triangle n$ = change in moles of gases in the reaction.

Calculation:

• The equation is: H2 + I2 = 2HI
• The equilibrium constant for the above reaction is:

$K_C = {[HI]^2 \over [H_2][I_2]}$
where [HI], [H2], [I2] are the concentration of the reactants and products expressed in moles/litre or mol litre-1.

• Putting the dimension of the concentration units, in the above equation, we get:

$K_c = {({mol-litre^{-1}})^2\over (mol-litre^{-1})(mol -litre^{-1})}$

or, Kc = 1.

• Hence, the equilibrium constant has no dimension, or it is a dimensionless quantity.

Hence, the correct option is none of the above.