the activation energy for the decomposition of HI(g) to H2(g) and I2(g) is 186kj/mol. the rate constant at 555k is 3.42 x 10^-7 L/mol*s. What is the rate constant at 645K?
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To solve this problem, we can use the Arrhenius equation. The Arrhenius equation relates the rate constant (k) to the activation energy (Ea), the temperature (T), and the gas constant (R). The equation is as follows:
k = A * exp(-Ea / (R * T))
Where:
k = rate constant
A = pre-exponential factor (frequency factor)
Ea = activation energy
R = gas constant (8.314 J/(mol*K) or 0.008314 kJ/(mol*K))
T = temperature in Kelvin (K)
In order to find the rate constant at 645K, we need to determine the value of A. To do that, we can rearrange the equation as follows:
A = k * exp(Ea / (R * T))
Step 1: Convert the activation energy from kilojoules per mole (kJ/mol) to joules per mole (J/mol):
Ea = 186 kJ/mol = 186,000 J/mol
Step 2: Convert the rate constant at 555K from L/mol*s to 1/mol*s:
k1 = 3.42 x 10^(-7) L/mol*s
Step 3: Convert the gas constant from kJ/(mol*K) to J/(mol*K):
R = 0.008314 kJ/(mol*K) = 8.314 J/(mol*K)
Step 4: Calculate the value of A:
A = k1 * exp(Ea / (R * T1))
= 3.42 x 10^(-7) L/mol*s * exp((186,000 J/mol) / (8.314 J/(mol*K) * 555K))
Step 5: Calculate the rate constant at 645K:
k2 = A * exp(-Ea / (R * T2))
= A * exp(186,000 J/mol) / (8.314 J/(mol*K) * 645K))
Now we can substitute the values into the equations to solve for k2.