The activation energy of a reaction is 123.9 kJ, and frequency factor (A) is 5.77 x 1010 sec -1, at what temperature (in Celsius) is the rate constant equal to 0.08103 sec-1?

Question

Enter your answer to the nearest whole number.

(Answer has to be in Celsius please)

Answer 1

NOTE: When you wrote, "activation energy is123 kJ, and frequency factor (A) is 5.77 x 1010 sec -1", I am assuming that: 1) 123kJ is 123 kJ/mol, and 2) 5.77 x 1010 sec -1 is 5.77*10¹⁰ s^-1

To solve this problem you need to use the Arrhenius Equation. This equation is usually presented in two way:

1. k = A * e ^{− [ Ea / (R * T) ]}

2. ln (k/A) = − (E_a / R*T)

We can use either variation. However, we must use algebra to separate for our variable of interest which in this case is temperature (T).

3. ln (k/A) = − (E_a / R*T) → T = − E_a / [ln (k/A) * R]

Once we have isolated our unknown variable we are almost ready can plugin our known values. These are rate constant (k), frequency factor (A), gas constant (R), and activation energy (E_a). The last thing we have to do before plugin into our equation for temperature is make sure the units on our R and E_a are the same for Joules. In order to do this, we will change the E_a from kJ/mol to J/mol.

E_a = 123.9 kJ/mol * (10³ J / 1 kJ) = 123900 J/mol

E_a = 123900 J/mol

Finally, we plug into our equation for the temperature:

T = − E_a / [ln (k/A) * R] → T = − 123900 (J/mol) / [ln(0.08103 s^-1 / 5.77*10¹⁰ s^-1) * 8.314 J/(K*mol)]

T = 558.1 °K − 273.15 = 284.95 °C

T = 284.95 °C

Answer 2

Use the Arrhenius equation k = A e-^E/RT. Take the natural log of each side.

lnk = lnA + ln e-^E/RT = lnA - E/RT

lnk - lnA = - E/RT Solve for T. (ln k - ln A = ln k/A)

T = - ( E / R ln k/A) Substitute the known parameters into this equation.

E = 123.9 x 10³ joules/mol, R = 8.314 j/mole-K, A = 5.77 x 10¹⁰ sec^-1, k = 0.08103 sec^-1

Change degrees K to degrees C.