Answer :
The formula for Keq for the first chemical reaction with given Keq is:
Keq 1 = [ HI ]^2 / [ H2 ] [ I2 ]
While the formula for Keq for the 2nd is:
Keq 2 = [ HI ] / [ H2 ]^(1/2) [ I2 ]^(1/2)
We can see that the coefficients in the reaction are equal to the exponents in the equilibrium equation. Therefore if we divide the whole reaction by 2, then that means we have to take the square root of the equilibrium equation. Or in this case,
Keq 2 = sqrt (Keq 1)
Keq 2 = sqrt (794)
Keq 2 = 28.19
The value at which the chemical reaction is at equilibrium and denoted in the form of a reaction quotient is called the equilibrium constant (Keq).
The Keq for the second reaction will be 28.
The calculations for Keq are as follows:
- The Keq for the first reaction [tex]\rm H_{2} (g) + I_{2} (g) \leftrightharpoons 2HI (g)[/tex] :
[tex]\rm Keq (1 )= \dfrac{[ HI ]^{2} }{[ H_{2} ] [ I_{2} ]}[/tex]
- For the second reaction [tex]\dfrac{1}{2} \rm H_{2} (g) + \dfrac{1}{2} \rm I_{2} (g) \leftrightharpoons HI (g)[/tex] :
[tex]\rm Keq (2) = \dfrac{[ HI ] }{[ H_{2} ]^{(\frac{1}{2})} [ I_{2} ]^{(\frac{1}{2})}}[/tex]
- From both the reactions we can see that the coefficients are the same as the components of equilibrium equations.
Therefore, we will:
[tex]\rm Keq (2) = \sqrt{Keq 1}[/tex]
We know that Keq (1) = 794
So,
[tex]\rm Keq (2) = \sqrt{794}[/tex]
[tex]\begin{aligned}\rm Keq (2) &= 28.19\\&=28\end{aligned}[/tex]
Therefore, Keq for the second reaction will be 28.
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