Cobra venom helps the snake secure food by binding to acetylcholine receptors on the diaphragm of a bite victim, leading to the loss of function of the diaphragm muscle tissue and eventually death. In order to develop more potent antivenins, scientists have studied what happens to the toxin once it has bound the acetylcholine receptors. They have found that the toxin is released from the receptor in a process that can be described by the rate law Rate \(=k[\) acetylcholine receptor-toxin complex \(]\) If the activation energy of this reaction at \(37.0^{\circ} \mathrm{C}\) is \(26.2 \mathrm{~kJ} /\) mol and \(A=0.850 \mathrm{~s}^{-1}\), what is the rate of reaction if you have a \(0.200-M\) solution of receptor-toxin complex at \(37.0^{\circ} \mathrm{C}\) ?

Step by step solution

01

Convert the temperature to Kelvin

To work with the Arrhenius equation, we need to convert our temperature from Celsius to Kelvin: \[ T = 37.0 + 273.15 = 310.15 K \]

02

Calculate the rate constant, k

The Arrhenius equation relates the rate constant to the activation energy and the temperature: \[ k = Ae^{\frac{-E_a}{RT}} \] where: - \( k \) is the rate constant we want to find - \( A \) is the frequency factor (0.850 s⁻¹) - \( -E_a \) is the activation energy (-26.2 kJ/mol) - \( R \) is the gas constant (8.314 J/mol·K) - \( T \) is the temperature in Kelvin (310.15 K) First, convert the activation energy from kJ/mol to J/mol: \[ E_a = 26.2 \times 1000 = 26200 J/mol \] Now, plug in the values into the Arrhenius equation: \[ k = 0.850e^{\frac{-26200}{(8.314)(310.15)}} \] Calculate k: \[ k = 1.713 \times 10^{-4} \, \mathrm{s}^{-1} \]

03

Calculate the rate of reaction

Using the given rate law and the calculated rate constant k, calculate the rate of the reaction with a 0.200 M solution of receptor-toxin complex: \[ \text{Rate} = k [\text{acetylcholine receptor-toxin complex}] \] Plug in the values: \[ \text{Rate} = (1.713 \times 10^{-4} \, \mathrm{s}^{-1})(0.200 \, \mathrm{M}) \] Calculate the rate of reaction: \[ \text{Rate} = 3.426 \times 10^{-5} \, \mathrm{M} \cdot \mathrm{s}^{-1} \] Therefore, the rate of reaction for a 0.200 M solution of receptor-toxin complex at 37.0 °C is \( 3.426 \times 10^{-5} \, \mathrm{M} \cdot \mathrm{s}^{-1} \).

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!