Dinitrogen tetroxide decomposes to nitrogen dioxide: N2O4( g) ¡ 2 NO2( g) ΔHrxn ° = 55.3 kJ At 298 K, a reaction vessel initially contains 0.100 atm of N2O4. When equilibrium is reached, 58% of the N2O4 has decomposed to NO2. What percentage of N2O4 decomposes at 388 K? Assume that the initial pressure of N2O4 is the same (0.100 atm).

Video transcript

Hi everyone here we have the questions giving us the following decomposition reaction Phosphorus four. Gashes forms to phosphorus two gashes And the change in entropy of our reaction is 229.1 kg joules. Our goal here is to calculate the percentage of 0.100 atmosphere phosphorus four that decomposed at 314 Kelvin at 47.00% of 0. atmosphere Phosphorus for decomposed to phosphorus to when equilibrium was reached at 298 Kelvin. So our step one is going to be to calculate the equilibrium constant at K. So our equilibrium constant is going to equal p p two squared divided by p a P four, which equals two Times 0. Times 0. squared divided by 0.100 times one minus zero 0.47, Equal 0.1667. And now we need to calculate the equilibrium constant at 394 Kelvin. So the natural log of K one plus our change in entropy of the reaction over our gas constant Times one over T one equals delta S. Of the reaction over our gas constant Equals the natural log of K two plus the change in entropy of the reaction over the gas constant Times one over T two. So the natural log of K two Equals the natural log of K one plus the change in entropy of our reaction over the gas constant Times one over T one -1 over T two. And that equals The natural log of K two equals natural log of zero point plus two .291 Times 10 to the 5th over 8.314, jules, thermals, times kelvin times one over 2 minus one over 314. And that gives us K two equals 18. 62. And now our last step, we're going to let x equal our percent decomposed Out of 100. So kate equals P p two squared divided by p p four equals two, X squared, divided by 0. minus X equals .5462. So for X two equals 18 0. Times 0.1 -X. So four x 2 minus 18.54 times X plus 18. times 0.1 equals zero, solving for X. We get X equals zero point zero 9793. And then changing that to 1%, we get zero divided by 0.1 times 100 equals .93%. And that is our final answer. Thank you for watching. Bye