A reaction has a rate constant of 0.0117s at 400.0 K and
0.689s...

Question

A reaction has a rate constant of 0.0117>s at 400.0 K and
0.689>s at 450.0 K.
a. Determine the activation barrier for the reaction.

Accepted Answer

hi everyone for this problem, it reads the rate constant values for a hypothetical reaction are 1.250 times 10 to the negative four seconds inverse and 8.764 times 10 to the negative three seconds inverse at 345 kelvin and 360 kelvin respectively, calculate the value of activation energy. So our goal here is to calculate our activation energy. And let's take a look at what we're given, were given to rate constants here. So we can say that this can be K one and this one will be K two were also given to temperatures that go with each of our rate constants. So this will be T one and this will be T two. So we're being asked to solve for the activation energy. Whenever we're given um rate constants at two different temperatures. There's an equation that we can use to solve for activation energy and that equation is Ln of K two over K one is equal to negative activation energy over r Universal gas constant Times one over T 2 -1 over T one. So we know all of these values except activation energy and we're going to be solving for activation energy. So let's go ahead and plug in what we know, we said, K2 is eight 764 times 10 to the negative three seconds inverse and K one is 1.250 times 10 to the negative four seconds inverse are negative activation energy is what we're solving for. So we'll leave that there. R universal gas constant is a value that we should know, it's not going to be given in the problem. And that value is 8. jewels over mall times, kelvin times one over T two. We said T two is 360 kelvin minus one over T one, which we said is 345 kelvin. So we have everything plugged in. So let's go ahead and simplify. The left side becomes 4.250 and our right side becomes activation energy times 1.453 times 10 to the negative five. So we just simplified a little bit here. So let's go ahead and divide both sides by 1.453 times 10 to the negative five. So that we can isolate our activation energy. Okay, Okay, so when we simplify that out, we get our activation energy is equal to 290, jewels per mole. We can simplify this by going from jewels to kill a jewels to make our numbers smaller. So in one, kill a jewel, we have 1000 jewels. Okay, so our jewels is going to cancel here and we'll be left with killer joules per mole. And when we simplify that out we get 292.5 kg jewels per mole. So our activation energy is 292.5 kg jewels per mole. And this is our final answer. This is the value of the activation energy. Given these rate constants and temperatures. That's the end of this problem. I hope this was helpful.

A reaction has a rate constant of 0.0117>s at 400.0 K and 0.689>s at 450.0 K. a. Determine the activation barrier for the reaction.

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