The rate constant of a first order reaction is 4.60x10^-4/s at 350 degrees Celsius. If the activation energy is 104 kJ/mol, calculate the temp. at which its rate constant is 8.80 x 10^-4/s.
So I think that I can use this version of the equation:
ln (k1/k2) = Ea/R * (T1-T2/T1*T2)
Because I am looking for T2.
But now how do I go about solving for T2 when it's in two different places like that?
How about trying this? k1, k2, Ea, R are known, so lets just use them as constants and call T1 something like 300.
ln K = k(300-X/300X)
?? = k(300-X/300X)
300X*??= k(300-X)
300X*?? = 300k - 300X
300*??*X + 300X = 300*k
Which is similar to
400X+300X = 400
700X = 400
X = 400/700
I know I have not made sense with the values but it shows you how to solve the problem.
Lnk1= LnA - Ea/R*T1
Lnk2= LnA - Ea/R*T2
lnK1- Lnk2 = LnA ¨CLnA +(- Ea/R*T1+ Ea/RT2)
Ln(K1/K2)= Ea/R*T2 ¨C Ea/R*T1
Ln(K1/K2)=(Ea/R)(1/T2-1/T1 )
1/T2= (Ln(K1/K2))(R/Ea)+1/T1
T2= (Ea*T1)/(Ln(K1/(K2 ))R*T1+Ea)
T1= 350¡ãC=350+273=623K
K1= 4.60*10-4 s-1
K2= 8.80*10-4s-1
Ea=104Kj/mol
R=8.314j/k.mol because of Ea, R=8.80*10-3kj/k.mol
T2=(104*623)/(Ln((4.60*¡¼10¡½^(-4) s^(-1))/(8.80*¡¼10¡½^(-4)*s^(-1)))*8.314*¡¼10¡½^(-3)*623+104)
T2=643.780K= 644k
644-273=371
T2= 371¡ãC
Thank you. PIERRE
There is some add of some messing letters from the system. Please, move them away to get the correct result. Thank you !!!
To solve for T2 in the equation ln(k1/k2) = Ea/R * (T1-T2/T1*T2), we can rearrange the equation and isolate T2.
Let's start by rearranging the equation:
ln(k1/k2) = Ea/R * (T1 - T2) / (T1 * T2)
Next, multiply both sides of the equation by (T1 * T2):
ln(k1/k2) * (T1 * T2) = Ea/R * (T1 - T2)
Expand the right side of the equation:
ln(k1/k2) * T1 * T2 = Ea/R * T1 - Ea/R * T2
Rearrange the equation to isolate T2 terms:
ln(k1/k2) * T1 * T2 + Ea/R * T2 = Ea/R * T1
Factor out T2:
T2 * (ln(k1/k2) * T1 + Ea/R) = Ea/R * T1
Now we can divide both sides by ln(k1/k2) * T1 + Ea/R to isolate T2:
T2 = (Ea/R * T1) / (ln(k1/k2) * T1 + Ea/R)
Plug in the given values: k1 = 4.60 x 10^-4/s, k2 = 8.80 x 10^-4/s, Ea = 104 kJ/mol, and R = 8.314 J/(mol·K).
T1 should be given in Kelvin. So if you convert 350 degrees Celsius to Kelvin, T1 would be 350 + 273.15 = 623.15 K.
Now substitute the values into the equation:
T2 = (104 kJ/mol / (8.314 J/(mol·K))) * 623.15 K / (ln(4.60 x 10^-4 / 8.80 x 10^-4) * 623.15 K + (104 kJ/mol / (8.314 J/(mol·K))))
Simplify the equation further and calculate T2 using a calculator.