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Ch.5 - Thermochemistry
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook
All textbooksBrown 14th EditionCh.5 - ThermochemistryProblem 13
Chapter 5, Problem 13

(a) What is the electrostatic potential energy (in joules) between an electron and a proton that are separated by 230 pm? (b) What is the change in potential energy if the distance separating the electron and proton is increased to 1.0 nm? (c) Does the potential energy of the two particles increase or decrease when the distance is increased to 1.0 nm?

Verified step by step guidance
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Step 1: Understand the concept of electrostatic potential energy, which is given by the formula: \(U = \frac{k \cdot q_1 \cdot q_2}{r}\), where \(k\) is Coulomb's constant (\(8.99 \times 10^9 \text{ N m}^2/\text{C}^2\)), \(q_1\) and \(q_2\) are the charges of the particles, and \(r\) is the separation distance between the charges.
Step 2: Identify the charges involved. For an electron, \(q_1 = -1.602 \times 10^{-19}\) C, and for a proton, \(q_2 = 1.602 \times 10^{-19}\) C. The separation distance \(r\) for part (a) is 230 pm, which needs to be converted to meters (1 pm = \(10^{-12}\) m).
Step 3: Calculate the electrostatic potential energy for part (a) using the formula from Step 1 with the given values for \(q_1\), \(q_2\), and \(r\).
Step 4: For part (b), calculate the potential energy again using the new separation distance of 1.0 nm (1 nm = \(10^{-9}\) m) and the same charges.
Step 5: Compare the potential energies calculated in parts (a) and (b) to determine the change in potential energy and whether it increases or decreases when the distance is increased to 1.0 nm.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Electrostatic Potential Energy

Electrostatic potential energy is the energy stored due to the position of charged particles relative to each other. It is calculated using the formula U = k * (q1 * q2) / r, where U is the potential energy, k is Coulomb's constant, q1 and q2 are the charges, and r is the distance between them. For an electron and a proton, this energy is negative, indicating an attractive force.
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Coulomb's Law

Coulomb's Law describes the force between two charged particles, stating that the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This law is fundamental in understanding how the distance between charges affects both the force and the potential energy in electrostatic interactions.
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Distance and Potential Energy Relationship

The relationship between distance and potential energy is crucial in electrostatics. As the distance between two opposite charges increases, the potential energy becomes less negative (or increases), indicating a decrease in the attractive force. This concept helps in understanding how changes in separation distance affect the stability and energy of charged systems.
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Related Practice
Textbook Question

(c) Does the potential energy of the two particles increase or decrease when the distance is increased to 1.0 nm?

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Textbook Question

Consider the two diagrams that follow. (d) Would similar relationships hold for the work involved in each process?

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Textbook Question

(b) What is the change in potential energy if the distance separating the two electrons is increased to 1.0 nm?

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Textbook Question

(a) What is the electrostatic potential energy (in joules) between two electrons that are separated by 62 pm?

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Textbook Question

In the accompanying cylinder diagram, a chemical process occurs at constant temperature and pressure. (a) Is the sign of w indicated by this change positive or negative?

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