If K_c = 7.5×10⁻⁹ at 1000 K for the reaction N₂(g) + O₂(g) → 2 NO(g), give the value of K_c at 1000 K for the reaction

(a) 2 NO(g) → N₂(g) + O₂(g)

Video transcript

Welcome back everyone. At 298 Kelvin, the equilibrium constant for the reaction two H two S produces two H two plus S two is 1.67 multiplied by 10. The power of negative seven. What is the KC for the reaction? H two S produces two and one half of a mole of S two at the same temperature? Now, let's take a look at the given reaction specifically, we're given an equilibrium reaction and it tells us that two moles of H two S for these two moles of age two and the one mole of S two, if we look at the target reaction, that's one mole of H two S produces one mole of H two plus one half of a mole of S two. And what we can notice is that the target equation has its coefficients halved relative to the given equilibrium, right? Specifically, if we multiply our reaction number one by one half, we get reaction number two. Now let's recall that whenever we are multiplying our coefficients by a specific number, we are using that number in the exponent uh within the relationship between the equilibrium constants now that might seem complicated, but let's analyze it. So let's suppose that the equilibrium constant of the first reaction is K one and the equilibrium constant of reaction number two is K two. Now K two is obtained by multiplying reaction number one by a specific number in this case, one half, right. So what we're going to do is take the equilibrium constant K one and raise it to the power of a one half. Because we have used that number as a multiplier in obtaining reaction number two. Now we know that exponent of one half essentially means taking square root. So we have our relationship and we can say that the equilibrium constant KC for reaction number two is simply square root of the equilibrium constant of reaction number one. So we're taking square root of 1.67 multiplied by its sense, the power of negative sevens. And if we evaluate the result, we get 4.09 multiplied by sense, the power of negative fourth, which is our final answer. Thank you for watching.