given temp. coeff. for saponificatn of ethyl acetate by naoh is 1.75.calculate activatn energy for reacn.

To calculate the activation energy for the saponification of ethyl acetate by sodium hydroxide (NaOH), we can use the Arrhenius equation, which relates the rate constant of a reaction to temperature and activation energy. The equation is given by:

Arrhenius Equation

The Arrhenius equation is expressed as:

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

Where:

• k = rate constant
• A = pre-exponential factor (frequency factor)
• E_a = activation energy (in Joules per mole)
• R = universal gas constant (8.314 J/(mol·K))
• T = temperature (in Kelvin)

Temperature Coefficient

The temperature coefficient (often denoted as Q10) indicates how the rate of a reaction changes with a 10°C increase in temperature. In this case, the temperature coefficient for the saponification of ethyl acetate by NaOH is given as 1.75. This means that for every 10°C increase in temperature, the rate of reaction increases by a factor of 1.75.

Calculating Activation Energy

To find the activation energy using the temperature coefficient, we can use the following relationship:

Q10 = e^(Ea/(R * 10))

Rearranging this equation gives us:

ln(Q10) = Ea/(R * 10)

From this, we can solve for the activation energy (E_a):

E_a = R * 10 * ln(Q10)

Substituting Values

Now, let's substitute the known values into the equation:

• R = 8.314 J/(mol·K)
• Q10 = 1.75

Calculating the natural logarithm of 1.75:

ln(1.75) ≈ 0.5596

Now, substituting these values into the equation:

E_a = 8.314 J/(mol·K) * 10 * 0.5596

E_a ≈ 46.5 J/mol

Final Result

Thus, the activation energy for the saponification of ethyl acetate by sodium hydroxide is approximately 46.5 kJ/mol. This value indicates the energy barrier that must be overcome for the reaction to proceed, reflecting the relationship between temperature and reaction rate in this specific chemical process.