Using data from Appendix C, write the equilibrium-constant expression and calculate the value of the equilibrium constant and the free-energy change for these reactions at 298 K: (a) NaHCO₃(s) ⇌ NaOH(s) + CO₂(g)

Video transcript

Hello everyone. So in this video we're trying to find the expression for the K. Constant of the reaction. We're also trying to find the value for that constant. And the delta G value for the reaction. And the temperature conditions were given is 2 kelvin's. So we know that our K constant is equal to the concentration of our products over the concentration of our reactant. And we only include those of the caucasus face. We can see that we only have one of that because our starting reagent and the other reagent here is going to be solid form and we only want the gas. So we do that. Then we just have that the K constant is solely dependent on the concentration of our S. 03. So let's see here, let's go ahead and sulfur are delta G. So delta G is equal to the delta G. Here of our products minus the delta G. Of our reactive And of course we're giving those values in the problem. Right over here we go ahead and use those then. So my delta G of the reaction is equal to negative 79.7 plus negative 71.1 minus. This is now of our reactant is negative 992.8. So putting all that into my calculator. I get the value for delta G. Of the reaction to be 242.0 units being killed. Jules per mole. Now we need to go ahead and suffer constant. How we can relate our delta G and the K constant. This of this reaction here, which is that delta G. A. Just do it to the right side. The delta G is equal to the negative art of T. Multiplied by the natural log of our cake constant. We can do some mathematical manipulation to go ahead and isolate for R. K. Value once we do so we get K. Is equal to erase the power of delta G. Over negative R. Of T. So we have all the components to fill that in. So let's go ahead and do that. I'll go ahead and fill out the denominator first. So we have again this negative the R value is 800 or 8.314 joules per mole times leader and R. T. Is our temperature. We said this to be 9 to 98 calvins. And our delta G we just solved for is 242. So we have this in killer jewels we wanted and jewels to be able to cancel out with the units of our. So we can just multiply this value by 1000 to get us to our jewels unit. So go ahead and put everything into my calculator. Once I do so I see that my K. Constant is equal to 3.7996 times 10 to the -43. So writing this in the correct amount of significant figures. We have four times 10° C. Power for -43. So my first answer is that my delta G value is equal to 242.0 killed, joules per mole. And my key concept here is four times 10 to the negative 43. That's going to be my final answer for this problem. Thank you all so much for watching.