Velocity constant of reaction at 290k was found to be 3.2*10^-3 At 300k it will be

To determine the velocity constant of a reaction at a different temperature, we can use the Arrhenius equation, which relates the rate constant (k) to temperature (T). The equation is expressed as:

Understanding the Arrhenius Equation

The Arrhenius equation is given by:

k = A * e^(-Ea/(RT))

• k = rate constant
• A = pre-exponential factor (frequency factor)
• e = base of the natural logarithm
• Ea = activation energy (in joules per mole)
• R = universal gas constant (8.314 J/(mol·K))
• T = temperature (in Kelvin)

From this equation, we can see that the rate constant increases with temperature, assuming that the activation energy remains constant. To find the rate constant at 300 K, we can use the concept of the temperature dependence of the rate constant.

Calculating the Rate Constant at 300 K

We can use the following simplified form of the Arrhenius equation to estimate the change in the rate constant with temperature:

ln(k2/k1) = -Ea/R * (1/T2 - 1/T1)

Where:

• k1 = rate constant at T1 (290 K)
• k2 = rate constant at T2 (300 K)
• T1 = initial temperature (290 K)
• T2 = final temperature (300 K)

We know:

• k1 = 3.2 x 10^-3
• T1 = 290 K
• T2 = 300 K

Estimating Activation Energy

To proceed, we need to estimate the activation energy (Ea). If we assume a typical value for many reactions, let's say Ea is around 50 kJ/mol (which is 50000 J/mol). We can now plug in the values:

Substituting Values into the Equation

Using R = 8.314 J/(mol·K), we can rearrange the equation to find k2:

First, we calculate:

ln(k2/k1) = -Ea/R * (1/T2 - 1/T1)

Substituting the values:

ln(k2/3.2 x 10^-3) = -50000/8.314 * (1/300 - 1/290)

Calculating the right side:

1/300 - 1/290 = (290 - 300) / (300 * 290) = -10 / 87000 ≈ -0.000115

Now substituting this into the equation:

ln(k2/3.2 x 10^-3) = -50000/8.314 * (-0.000115)

Calculating the left side:

ln(k2/3.2 x 10^-3) ≈ 0.676

Now, we can solve for k2:

k2 = 3.2 x 10^-3 * e^(0.676)

Calculating e^(0.676) gives approximately 1.968. Thus:

k2 ≈ 3.2 x 10^-3 * 1.968 ≈ 6.29 x 10^-3

Final Result

Therefore, the estimated velocity constant of the reaction at 300 K is approximately 6.29 x 10^-3. This calculation illustrates how temperature influences reaction rates and highlights the importance of the Arrhenius equation in predicting these changes.