At a temperature of 700 K, the forward and reverse rate constants for the reaction 2 HI(𝑔) ⇌ H₂(𝑔) + I₂(𝑔) are 𝑘_𝑓=1.8×10⁻³ 𝑀⁻¹s⁻¹ and 𝑘_𝑟 = 0.063  𝑀⁻¹s⁻¹. (b) Is the forward reaction endothermic or exothermic if the rate constants for the same reaction have values of 𝑘_𝑓 = 0.097 𝑀⁻¹s⁻¹ and 𝑘_𝑟 = 2.6 𝑀⁻¹s⁻¹ at 800 K?

Video transcript

Hello everyone today. We are being given the following problem and asked to solve for it. This is at 3 58 kelvin. The verification of an organic acid and an alcohol has a favored forward reaction rate constant of 2.25 times 10 to the negative fourth inverse units of malaria in seconds. And a reverse rate constant of 1.85 times 10 to the negative fourth inverse polarity and seconds when the temperatures increased to 3 kelvin. The rate constants for the same reaction have values of K F. For the forward reaction constant of 3.14 times 10 to the negative fourth inverse units of malaria in seconds. And KR, or the constant rate of the reverse reaction equaling 1.97 times 10 to the negative fourth inverse units of malaria and seconds is the reverse reaction endo thermic or exhaust thermic. So the first thing we want to do to solve this problem is we need to use the values given by KF and KR to calculate K C. And to calculate K C. That's going to be the constant of the forward reaction over the constant of the reverse reaction. And so we have to solve this at two different temperatures. And so we're going to solve for the KC at kelvin first. So we have our K F and r K R values what we saw for K C. We have K C is equal to 2.25 times to the negative fourth inverse units of molar itty and seconds. And that's going to be divided by r K r or 1.85 times 10 to the negative fourth inverse units of malarkey and seconds. And this is going to give us a total of 1.22. Now to solve for K C at Kelvin, We apply the same principles. So our case is going to be equal to RKF at 368, which is 3.14 times 10 to the negative fourth inverse units of malaria, T and seconds over 1.97 times 10 to the -4 Inverse units of maturity and seconds. And this gives us an answer of 1.59. And so a principle we want to make note of or a couple principles is that if the Casey is less than one, there are more reactant than products. If KC. is equal to one than the reactant or the amount of reactant is going to equal the amount of product and then if we have that K C. Is greater than one, we are simply going to have more products available. Now, another principle to note is that Casey indicates the extent of the forward reaction. So the extent of the forward reaction. And so in this reaction the value constant K C increases with temperature. So K C increases with increasing temperature. This basically means that the extent of the forward reaction is increasing and more product is formed when the temperature is increased. So when we go from this 358 Kelvin to R368 Kelvin, we are increasing the temperature present. And so this indicates that the forward reaction to the forward reaction is endo thermic because we are applying more heat to the system. And so if the forward reaction is endo thermic, then the reverse reaction must be the opposite or exhaust thermic, as in it releases heat. And that's going to be our final answer. I hope this helped handle next time.