If K c = 7.5×10 −9 at 1000 K for the reaction N 2 (g) + O 2 (g) → 2 NO(g), give the value of K c at 1000 K for the reaction (a) 2 NO(g) → N 2 (g) + O 2 (g)

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.

Ch.15 - Chemical Equilibrium

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McMurry 8th Edition

Ch.15 - Chemical Equilibrium

Problem 15.60a

Chapter 15, Problem 15.60a

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)

Verified step by step guidance

First, recognize that the second reaction is the reverse of the first reaction. In other words, the reactants and products have been swapped.

Next, recall that the equilibrium constant for the reverse reaction is the reciprocal of the equilibrium constant for the forward reaction. This is because the equilibrium constant is a ratio of the concentrations of the products to the reactants, so reversing the reaction swaps the numerator and denominator of this ratio.

Then, calculate the reciprocal of the given equilibrium constant, Kc, for the forward reaction. The reciprocal of a number is simply 1 divided by that number.

Finally, the reciprocal of Kc for the forward reaction is the value of Kc for the reverse reaction. This is the answer to the problem.

Remember, you don't need to calculate the exact value. The purpose of this problem is to understand the relationship between the equilibrium constants of forward and reverse reactions.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Equilibrium Constant (Kc)

The equilibrium constant, Kc, quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. It is expressed as Kc = [products]^[coefficients] / [reactants]^[coefficients]. A small Kc value, like 7.5×10^−9, indicates that at equilibrium, the concentration of reactants is much greater than that of products.

Reversibility of Reactions

Chemical reactions are often reversible, meaning the products can react to form the original reactants. The equilibrium constant for the reverse reaction is the reciprocal of the forward reaction's Kc. For the reaction 2 NO(g) → N2(g) + O2(g), the Kc can be calculated as 1/(7.5×10^−9), reflecting the relationship between the forward and reverse reactions.

Temperature Dependence of Kc

The value of the equilibrium constant, Kc, is temperature-dependent. Changes in temperature can shift the position of equilibrium and alter the concentrations of reactants and products. Therefore, when calculating Kc for a reaction at a different temperature, it is essential to consider that Kc values are specific to the temperature at which they are measured.