The value of K_a for nitrous acid (HNO₂) at 25 °C is given in Appendix D. (d) What is the value of ΔG when [H⁺] = 5.0⨉10^-2 M, [NO₂^-] = 6.0⨉10^-4 M, and [HNO₂] = 0.20 M?

Video transcript

hey everyone for this problem we're told that the hydraulic sis of a TP to ADP is an important reaction. And the production of energy to do work or drive chemical reactions in biological systems. And the reaction is shown below. They tell us that the standard gibbs free energy is negative 30 point five kg jewels at 37 degrees Celsius and a ph of seven. And we need to calculate what is the value of our gibbs. Free energy and killing joules per mole. And whether or not this is a spontaneous reaction under these conditions. So equation that relates gibbs free energy to standard gibbs. Free energy is our gifts. Free energy of our reaction is equal to our standard gibbs. Free energy plus R. T. Ln of Q. And here we are solving for the value of our gibbs free energy. They tell us that our standard gibbs free energy is negative 30.5. Our is our constant 8.314 joules. Per mole, kelvin, T. Is our temperature which they give us. And Ellen is a function on our calculator. Q. Is our concentration of products over our concentration of reactant sits a constant and we can go ahead and plug in what we know based off what's given in the problem. So our delta G. Of our reaction is going to be our data G. Not which is negative 30.5 killer jewels. Now we're going to need to convert this to jules And we can do that by multiplying that by 1000 and so we get negative 30, 500 jules Permal. And the reason that we converted that to jules you'll see is because our our has a are constant, has the units jewels per mole kelvin, so plus our Is 8. jules per mole Calvin. They tell us that our temperature is 37°C. And because our our has the unit Kelvin, we need to convert this degree C to Kelvin and we can do that by adding 273.15. And when we do that we get our temperature in Kelvin is 0.15 Calvin. Okay and now we have Ln of Q. So our Q. Is going to equal concentration of products over concentrations of reactant. And we're going to use our balanced chemical equation that they gave us to plug in the concentrations paying attention to our coefficients. So we have a coefficient of one for everything. And for our Q we don't include liquids so we can go ahead and cross out our water. So when we plug in our values we get Ln of concentration of products over concentration of reactant. So for our products we have two ADP is the first one we have ADP is 0.25 million moller and we need to convert this into moller. So for all of them we are going to multiply by 10 to the negative three because one million moller is equal to 10 to the negative three Moeller. So for our ADP we get 2.5 Times 10 to the -4 Moeller and HP 042 is 1.65 million moller. And so we get 1.65 times 10 to the negative three molar. So we need to make sure we do that conversion and not just plug in the middle moller. And this is all over concentration of our reactant. So we only have one reactant that we're going to include here because we eliminated our water because it's a liquid. So r http has a concentration of 2.25 and when we multiply that by 10 to the negative three we get 2.25 times 10 to the negative three. So that is our cue. So let's go ahead and simplify here so that we can solve so we can go ahead and simplify by multiplying these two and by multiplying out our cue and when we simplify We get delta g of our reaction is equal to negative 30,500 jewels per mole plus our kelvin's are going to cancel here. And when we simplify that out we get 587 jules per mole. And then that's going to be L. N. And let's simplify Our cue here. And when we do that we get 1. Times 10 to the -4. Okay, so now let's keep going with our simplification, we get negative 30, 500 jules per mole. And we can simplify by solving for R. L. N. Of 1.83 times 10 to the -4. And we're going to multiply that by 2,578.587. And when we do that we get plus negative 22191. So we're almost done here. Once we calculate this, we get a final answer of delta G of our reaction is negative 5,052, 691 Jules. And here they are asking for the value and killing joules per mole so we can go ahead and say that in one kill a jewel. We have 1000 jaws, our jewels cancel. And we're left with an answer of -52.7. Kill the jewels and this is our final answer. This is our value of our gibbs. Free energy for this reaction. I hope this was helpful