Arrhenius Equation Example 2

by Jules Bruno
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a chemical reaction has rate constants of 4.6 times 10 to the negative two seconds inverse and 8.1 times 10 to negative two seconds inverse at zero degrees Celsius and 20 degrees Celsius respectively. What is the value of the activation energy? Alright, so they're giving us to rate constants since this one has stated first, this is K one And this would have to be K2, respectively. Would mean that zero degrees is connected to K one and therefore would be T one And the second temperature will be connected to K two and therefore it is T two. Now we'd say here that Ln of K two over K one equals negative E A over R times one over T two minus one over T one. Here, we're gonna place the numbers that we have. So it's Ln of so K two is 8.1 times 10 to the negative two, divided by 4.6 times 10 to the negative two. We're looking for activation energy. So, e is what we need to find our here is our gas constant, which is 8.314 jewels over moles, times K times We're gonna say one over T two. So remember we have to add to 73.15 to each one of these Calvin temperatures. So when we do that, this becomes to 93.15 k minus one over To 73.15 K. Mhm. Here we're going to do Ln of eight K two over K one. When we do that we're going to get as our answer 10.4 point 565808 equals. Alright. So E. A. It's gonna be multiplying by what's in here. So when we do that we're gonna get uh negative value in here. So this is gonna be what's in here is equal to negative 2.49769 times 10 to the negative four A negative times a negative gives me positive. That'd be positive E. A. Times 2.49769 times 10 to the negative four Divided by still 8.314. Here we're going to multiply both sides by 8.314. So when we do that we're gonna get 4. equals E. A. Still times 2.49769 times 10 to the negative four, divide both sides now By 2.4976. 9 times 10 to the -4. So when we do that we're gonna get our E. A. Which I'm gonna right over here. So er here equals 18,833.91 jules per mole. Now if we go back up here this has two sig figs to 6 to figs for 4.6 and 8.1. Let's not worry about the temperatures. So let's just do this in terms of two sig figs. So that will become 1.9 times 10 to the four jewels per mole. So this would be our value for activation energy, abbreviated as e a.