The equilibrium 2 NO(𝑔) + Cl₂(𝑔) ⇌ 2 NOCl(𝑔) is established at 500.0 K. An equilibrium mixture of the three gases has partial pressures of 0.095 atm, 0.171 atm, and 0.28 atm for NO, Cl₂, and NOCl, respectively. (b) If the vessel has a volume of 5.00 L, calculate Kc at this temperature.

Video transcript

Hey, everyone, we're asked to consider the following equilibrium. We're told that at 600 Kelvin, the partial pressures of the three gasses in the equilibrium mixture, nitric oxide bromide and nitrous il bromide are with 0.1 atmospheric pressure, 0.1 15 atmospheric pressure and 0.348 atmospheric pressure respectively determine the value of our equilibrium constant at this temperature. To answer this question, we first need to calculate our equilibrium constant calculated by the partial pressures since they provided us with the partial pressures. So this is going to be the partial pressure of our products divided by the partial pressure of our reactant. Now, in terms of our reaction, this is going to look like the partial pressure of our nitrous il bromide. And this is going to be squared. Since we have that coefficient of two in our reaction, This will be divided by the partial pressure of our nitric oxide, which will be squared as well due to that coefficient of two times the partial pressure of our bromide. So now let's go ahead and plug in these values. We have 0.348, which is the partial pressure of nitrous Il bromide. And this will be squared divided by the partial pressure of nitric oxide, which is said to be 0.150, which will be squared as well. And this is going to be multiplied by the partial pressure of bromide which is 0.115. Now, when we calculate this out, this comes up to a value of 46.8035. Now that we have the equilibrium constant calculated from our partial pressures, we're going to calculate our equilibrium constant, which is our KC and this is equal to our KP times our gas constant times our temperature. And this is going to be raised to the power of our change in our moles. So as we know our change in the number of moles is going to be the sum of the moles of our products minus the sum of the moles of our reactant plugging in these values. We see that we have that too from that nitrous il bromide. And we're going to subtract the sum of the moles of our reactant. So we have two from our nitric oxide plus one from our bromide. This gets us to a value of -1. Now let's go ahead and plug everything in. So to calculate our equilibrium constant at this temperature, we have the equilibrium constant from our partial pressures, which is said to be 46.8035. And we're going to multiply this by our gas constant, which is 0.08-0 six. And this is going to be multiplied by our temperature, which was said to be 600 Kelvin. Now, this will be raised to the value of that change in the number of moles which is -1. So when we calculate this out, we end up with a value of 9.51 times 10 to the negative one, which is going to be our final answer. Now, I hope this made sense and let us know if you have any questions.