Chapter 16: Q16.108 CP (page 734)

Assume water boils at $100^{0} C$ in Houston (near sea level), and at $90^{0} C$ in Cripple Creek, Colorado (near 9500 ft). If it takes 4.8 min to cook an egg in Cripple Creek and 4.5 min in Houston, what is $E_{a}$ for this process?

Short Answer

Expert verified

The activation energy $E_{a}$ is $7.3 \times 10^{3} J / m o l$ .

Step by step solution

Step 1: The Arrhenius equation

The Arrhenius equation is written like this:

$k = A e^{- E_{a} / R T} l n k = l n A - E_{a} / R T$

Where k is the rate constant, A is the frequency factor, $E_{a}$ is the reaction's activation energy at a certain temperature T, and R is the gas constant.

Step 2: Determine the activation energy

Write the equation for the two rate constants, $k 1$ and $k_{2}$ at temperature $T_{1}$ and $T_{2}$ respectively and obtain new expression:

$\ln k_{1} = \ln A - E_{a} / R T_{1} \ln k_{2} = \ln A - E_{a} / R T_{2} \ln k_{2} - \ln k_{1} = - \frac{E_{a}}{R} (\frac{1}{T_{1}} - \frac{1}{T_{2}}) \ln (\frac{k_{2}}{k_{1}}) = - \frac{E_{a}}{R} (\frac{1}{T_{1}} - \frac{1}{T_{2}})$

Substitute the values and determine the activation energy $E_{a}$

$\ln (\frac{1 e g g / 4.5 \min}{1 e g g / 4.8 \min}) = - \frac{E_{a}}{8.314 J / m o l . K} (\frac{1}{(273 + 90.0) K} - \frac{1}{(273 + 100.0) K}) E_{a} = \frac{(8.314 J / m o l . K) \ln (\frac{4.8}{4.5})}{(\frac{1}{363.2 K} - \frac{1}{373.2 K})} = 7.3 \times 10^{3} J / m o l$

Therefore, the activation energy is $7.3 \times 10^{3} J / m o l$ .

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Assume water boils at $100^{0} C$ in Houston (near sea level), and at $90^{0} C$ in Cripple Creek, Colorado (near 9500 ft). If it takes 4.8 min to cook an egg in Cripple Creek and 4.5 min in Houston, what is $E_{a}$ for this process?

Short Answer

Step by step solution

Step 1: The Arrhenius equation

Step 2: Determine the activation energy

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Assume water boils at 1000C in Houston (near sea level), and at 900C in Cripple Creek, Colorado (near 9500 ft). If it takes 4.8 min to cook an egg in Cripple Creek and 4.5 min in Houston, what isEa for this process?

Short Answer

Step by step solution

Step 1: The Arrhenius equation

Step 2: Determine the activation energy

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Chemistry Textbooks

Chemical Reactions

Chemical Analysis

Nuclear Chemistry

Making Measurements

Inorganic Chemistry

Physical Chemistry

Study anywhere. Anytime. Across all devices.

Assume water boils at $100^{0} C$ in Houston (near sea level), and at $90^{0} C$ in Cripple Creek, Colorado (near 9500 ft). If it takes 4.8 min to cook an egg in Cripple Creek and 4.5 min in Houston, what is $E_{a}$ for this process?