Urea (NH2CONH2), an important nitrogen fertilizer, is produced industrially by the reaction Given that ∆G° = -13.6 kJ, calculate ∆G at 25 °C for the following sets of conditions. . (a) 10 atm NH3, 10 atm CO2, 1.0 M NH2CONH2 (b) 0.10 atm NH3, 0.10 atm CO2, 1.0 M NH2CONH2 Is the reaction spontaneous for the conditions in part (a) and/or part (b)?

Video transcript

Hello everyone today. We have the following problem. Formic acid is the simplest carb oxalic acid and can be synthesized by the oxidation of formaldehyde. What is the value of the change in the Gibbs free energy for the reaction at 300° Kelvin. Under the following conditions we have the gibbs free energy for our system and then we have the volume at one leader. So first we will solve for our first condition. Before we do that, we need to evaluate the relationship between our gibbs free energy or our total gibbs free energy and the gibbs free energy for our system. And that is the gibbs free energy or the total gibbs Free energy is equal to the gibbs free energy of our system. Plus r gas constant R times r temperature times our natural log of Q. And so we need the natural log of Q. To solve for this, that is going to be the concentration of our products, divided by the concentration of our reactant. So for condition one our cue would be the concentration of products which is going to be our formic acid. No, there there's a 2. 1 as a coefficient. That's gonna become an exponent. And that's going to be divided by the concentration of our reactant which our first one is formaldehyde. No, there is a two as a coefficient. So that becomes an exponent. And then we have oxygen. And so we're simply going to plug in the moles for each of these values. So for formic acid we have 0.150 moles. We're gonna square that. Then for our formaldehyde we have .451 moles. And then for oxygen we have 0.852. That value is going to come out to 0.13 for our value of Q. So now we have to evaluate our total Gibbs free energy for condition one. And we're gonna use the formula that we came up with at the beginning of this problem. So we're gonna have our total gibbs. Free energy is equal to the gibbs free energy of our system plus r. Gas constant times temperature times our value of Q. So our gibbs free energy of the system is negative 5 killer joules per mole Plus our gas constant, which is 8.3 times 10 to the negative third. Kill it jules, per mole kelvin. We're gonna multiply that bar temperature of 300° Kelvin. And then our natural log, of course of 0. This is going to give us an answer of negative killed jules per mole. Considering the fact that we have a negative gifts for energy, this is going to indicate that we have a spontaneous reaction for our first condition. So Moving on to our 2nd condition, we're going to calculate Q. Just as before we're going to have our concentration of our formic acid. Don't you care that we're gonna divide that by the concentration of our formaldehyde, which is also squared times our concentration of oxygen Gas. We're going to plug those values in for our formic acid. We're going to have 0.950 moles For our formaldehyde. We're going to have .350 moles. And for oxygen we're going to have 1.54 moles. We plug this into our calculator, we're going to get 5.07 as our value of Q. As before. We're gonna plug in. Our equation are total gibbs. Free energy is to go to the gibbs. Free energy of our system plus r gas constant times our temperature times our natural log of Q. As before we had 5 18 kg joules per mole plus r gas constant 8.3 times 10 to the negative third killer, joules per mole kelvin. We multiplied by a temperature of 300 Kelvin. And then our natural log of 5. Plugs into our calculator. We're going to get a value of -514 kg per mole. As you said before, a negative total gives her energy is going to indicate that we have a spontaneous Reaction for our 2nd condition. And so both of these conditions are going to be spontaneous. And with that we have our final answers overall, I do hope this helped. And until next time