Question

The rate constant for a reaction at 25.0 degrees Celsius is 0.010 s-1 and its activation energy is 35.8 kJ. Find the rate constant at 50.0 degrees Celsius.

Answer 1

To determine the rate constant at 50.0 degrees Celsius, we use the Arrhenius equation with the given activation energy and the rate constant at 25.0 degrees Celsius. The process involves calculating the frequency factor at the initial temperature and then using it to find the rate constant at the higher temperature.

Step-by-step explanation:

To determine the rate constant at 50.0 degrees Celsius when it is 0.010 s-1 at 25.0 degrees Celsius with an activation energy of 35.8 kJ, we can use the Arrhenius equation:

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

Where:

k is the rate constant,

A is the frequency factor,

Ea is the activation energy,

R is the ideal gas constant (8.314 J/mol K), and

T is the temperature in Kelvin.

First, we'll convert the temperatures from Celsius to Kelvin:

T1 = 25.0 °C + 273.15 = 298.15 K

T2 = 50.0 °C + 273.15 = 323.15 K

Then, using the Arrhenius equation and solving for A at T1:

A = k / e^(-Ea/(RT1))

Now, with A determined, we can find the rate constant at T2:

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

This step-by-step process calculates the rate constant at a different temperature using known values and the Arrhenius equation. The key variables in this equation are the pre-exponential factor, the activation energy, and the temperature.

Answer 2

To find the rate constant at 50 degrees Celsius, we can use the Arrhenius equation.

Step-by-step explanation:

To find the rate constant at 50.0 degrees Celsius, we can use the Arrhenius equation:

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

Where:

• k2 is the rate constant at the new temperature (50.0 degrees Celsius)
• k1 is the rate constant at the initial temperature (25.0 degrees Celsius)
• Ea is the activation energy (35.8 kJ)
• R is the gas constant (8.314 J/K*mol)
• T1 is the initial temperature in Kelvin (25.0 degrees Celsius + 273.15 = 298.15 K)
• T2 is the new temperature in Kelvin (50.0 degrees Celsius + 273.15 = 323.15 K)

Plugging in the values:

k2 = 0.010 s⁻¹ * exp((35.8 * 10³ J) / (8.314 J/K*mol) * ((1 / 298.15 K) - (1 / 323.15 K)))

k2 = 0.072 s⁻¹