The rate constant for the first-order decomposition of gaseous N₂O₅ to NO₂ and O₂ is 1.7 * 10-3 s-1 at 55 °C. (b) Use the data in Appendix B to calculate the initial rate at which the reaction mixture absorbs heat (in J/s). You may assume that the heat of the reaction is independent of temperature.

Video transcript

Hello. In this problem, we're told an initial concentration of 0.199 dolar di nitrogen tetroxide was in a 1.5 liter container, assuming that the heat of reaction is temperature independent. Were asked to determine the initial rate at which the first order decomposition of di nitrogen tetroxide in two moles of nitrogen dioxide absorbs heat. Consider the rate constant value for this reaction as 3.4 times 10 to minus four per second. And the heat of the reaction is 5.5, 3 times 10-4 jewels per mole. Let's begin by writing down what we're given. So, you know, then the initial concentration of diet nitrogen tetroxide, 0.0199 Mueller At the volume of our container is 1.5 L. Our reaction rate constant is 3.4 times 10 to the -4/s. And the heat of reaction Is equal to 5.53 times 10 to the four jewels per mole. So let's find the initial rate. So the initial rate then is going to be equal to the reaction rate constant times our initial concentration of di nitrogen tetroxide. So this will be equal to 3.4 times 10 to the minus four per second times our concentration of 0.199 Mueller. So this works out to 6.76, 6 times 10 to the -6 Mueller per second. And now we're gonna find the initial rate at which the reaction absorbs heat. And this can be found by taking the initial rate times the volume times the entropy or heat of reaction. So we have our rate initially then which is 6.766 times 10 to minus six clarity per second times are volume, which is 1.5 liters. And the FP or heat of reaction, which is 5.53 times 10 to the four jules from all. And so we have moles and leaders. So leaders per mole is the inverse of polarity so that cancels with our similarity and we're left with joules per second. So this works out to 0.56 tools per second. So this is our initial rate reaction That absorbs heat. And when we look at the possible answers, we see that that matches d. So the initial rate at which the first order decomposition absorbs heat is .56 joules per second. Thanks for watching. Hope this helps