Consider the two reactions:
O + N₂ → NO + N E_a = 315 kJ/mol
Cl + H₂ → HCl + H E_a = 23 kJ/mol
b. The frequency factors for these two reactions are very close to each other in value. Assuming that they are the same, calculate the ratio of the reaction rate constants for these two reactions at 25 °C.

Question

Consider the two reactions:

O + N₂ → NO + N E_a = 315 kJ/mol

Cl + H₂ → HCl + H E_a = 23 kJ/mol

b. The frequency factors for these two reactions are very close to each other in value. Assuming that they are the same, calculate the ratio of the reaction rate constants for these two reactions at 25 °C.

Accepted Answer

hey everyone in this example we need to determine the ratio of the rate constants for our given reactions at 30 degrees Celsius. We need to also assume that both reactions have the same pre exponential factor. So looking at reaction one which will label here we would take its rate constant K one and set that equal to Ulis number were in our exponents. We're going to take the entropy of our first reaction given as negative 100 kg joules per mole which we want to convert to jules by converting from kilo joules in the denominator two jewels in the numerator, recalling that are prefix kilo, tells us that we have 10 to the third power jewels. And then we will multiply or rather divide In our exponents still buy our gas constant R which we recall is 8.314 jules Permal. And this is then multiplied by our temperature which according to the pump is 30°C and converting to Kelvin, we would add to 73.15 to get to our Kelvin temperature of 303.15 Kelvin. So just to be clear this is 2 73 Plus to 73.15 to give us our Kelvin temperature below. So we're going to plug this in 303.15 Kelvin. And so this is all for our exponents which is to us number. And so what we're going to get for our great constant from reaction one is a value of 5.87. Sorry. So it's five and my pen is messing up. So 5.87 times 10 to the negative 18th power. As far as units will be able to get rid of kila jules. We're going to be able to get rid of jewels, We're going to be able to get rid of moles and we're left with kelvin but the rate constant does not have units. So we're just going to disregard that. So moving on to our second rate constant for our second reaction, which we'll label to here where we have X plus Y producing Z. We're going to take you alors number and in our exponents we have the activation energy given for reaction to as 18 kayla jules Permal, we're going to make this a negative value since we will lose energy. And just as before we want to convert from kilo jewels into jewels. So our prefix kilo tells us we have 10 to the third power jewels. And then we're going to divide this still in the exponents by our gas constant. R 8.314 joules per mole And then multiply by our temperature in Kelvin which should still be 303.15 Kelvin according to the prompt. And so now we have all of this in our exponents and for our second value or for the rate constant for the second reaction. Rather we're going to have a value of zero point or rather let's write this in scientific notation. So it will be 7.913 six times 10 to the negative 4th power. So when we want to find the ratio of our rate constants were just going to divide K one by K two, which would be 5.87 times 10 to the negative 18th power divided by 7.9136 times 10 to the fourth to the negative fourth power. And this is going to give us the ratio of a rate constant equal to 7.41. Or we that we can round it to 7.42 actually Times 10 to the -15 Power. And that should be a 15 there for our ratio of our rate constant as our final answer. So what's highlighted in yellow is the ratio of our rate constants as we've calculated here. So I hope that everything I explained was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video.

Verified Solution

Key Concepts

Arrhenius Equation

Activation Energy (Ea)

Reaction Rate Constant (k)