The ratio of the rate constant of a reaction at two temperatures differing by __________0C is called temperature coefficient of reaction.a)2b)10c)100d)50Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Explanation: Half-life period of a first order reaction is directly proportional to the rate constant. So, it increases with increase in temperature.

Answer

For every 10° C rise in temp, the reaction becomes twice i.e 2× the initial rate( and sometimes even thrice).
The ratio of the rate constant at the initial temperature and the temp 10°C higher is the temp. coeff. of the reaction.

Answer

The temperature coefficient of a reaction is a measure of how the rate constant of a reaction changes with temperature. It is expressed as the ratio of the rate constant at two temperatures differing by a specific temperature interval. In this case, the temperature interval is 10°C.

To calculate the temperature coefficient of a reaction, we use the Arrhenius equation:

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

Where:
- k is the rate constant
- A is the pre-exponential factor (also known as the frequency factor)
- Ea is the activation energy
- R is the ideal gas constant
- T is the temperature in Kelvin

Now, let's consider two temperatures, T1 and T2, differing by 10°C. The ratio of the rate constants at these temperatures can be denoted as:

k2/k1 = (A * e^(-Ea/RT2))/(A * e^(-Ea/RT1))

Since the pre-exponential factor cancels out, we can simplify the equation to:

k2/k1 = e^(-Ea/R) * e^(Ea/T1) * e^(-Ea/T2)

Now, let's take the natural logarithm of both sides to eliminate the exponential terms:

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

We can rewrite this equation as:

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

Now, let's rearrange the equation to solve for the temperature coefficient:

k2/k1 = e^(-Ea/R * (T1 - T2)/(T1 * T2))

The temperature coefficient is given by the ratio of the rate constants, so:

Temperature coefficient = k2/k1 = e^(-Ea/R * (T1 - T2)/(T1 * T2))

Since the temperature interval in this case is 10°C, the correct answer is option 'B' (10).

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