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The equilibrium constant gives the relation between the product formation and the reactant used. The concentration of the dinitrogen tetroxide is 0.003 M, and nitrogen dioxide is 0.054 M.
An equilibrium constant gives the conversion rate of the reactant of the chemical reaction into the products.
The reaction can be shown as,
[tex]\rm N_{2}O_{4} \rightleftharpoons 2NO_{2}\;\; \rm Kp = 4.5[/tex]
From the ICE table attached below, the concentrations are calculated as:
[tex]\begin{aligned}\rm Kp &= \rm \dfrac{[NO_{2}]^{2}}{N_{2}O{4}}\\\\4.5 &= \rm \dfrac {x^{2}}{(0.0550 - x)}\\\\\rm x^{2} &=\rm 4.5 (0.0550 - x)\end{aligned}[/tex]
Solving further,
[tex]\begin{aligned} \rm 0.2475 - 4.5 x &= \rm x^{2}\\\\\rm x^{2} + 4.5 x - 0.2475 &= 0\\\\\rm x &= 0.054\end{aligned}[/tex]
Therefore, the concentration of nitrogen dioxide is 0.054 M and dinitrogen tetroxide is 0.003 M.
Learn more about the equilibrium constant here:
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