Consider the combustion of a single molecule of CH₄(g), forming H₂O(l) as a product. (b) A typical X-ray light source has an energy of 8 keV (see inside back cover for conversion between eV and J). Is the energy released by the combustion of a CH₄ molecule larger or smaller than the energy of an X-ray from this source?

Verified step by step guidance

Step 1: Write the balanced chemical equation for the combustion of methane (CH_4). The reaction is: CH_4(g) + 2O_2(g) -> CO_2(g) + 2H_2O(l).

Step 2: Determine the energy released by the combustion of one mole of CH_4. This is typically given as the standard enthalpy change of combustion (ΔH_comb) for methane, which can be found in thermodynamic tables.

Step 3: Convert the energy released per mole of CH_4 to energy released per molecule. Use Avogadro's number (6.022 x 10^23 molecules/mol) for this conversion.

Step 4: Convert the energy of the X-ray light source from keV to joules. Use the conversion factor: 1 eV = 1.602 x 10^-19 J.

Step 5: Compare the energy released per molecule of CH_4 with the energy of the X-ray. Determine if the energy released by the combustion is larger or smaller than the energy of the X-ray.

Key Concepts

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

Combustion Reaction

Combustion is a chemical reaction that typically involves the reaction of a hydrocarbon with oxygen to produce carbon dioxide and water, releasing energy in the form of heat and light. In the case of methane (CH4), the reaction can be represented as CH4 + 2O2 → CO2 + 2H2O. Understanding the stoichiometry and energy changes associated with this reaction is crucial for comparing the energy released to other forms of energy, such as X-ray photons.

Energy Units and Conversion

Energy can be expressed in various units, including electronvolts (eV) and joules (J). In this context, 1 eV is equivalent to approximately 1.6 x 10^-19 J. The question involves comparing the energy released from the combustion of methane to the energy of X-ray photons, which are typically measured in keV (kiloelectronvolts). Understanding how to convert between these units is essential for making accurate comparisons.

Energy of X-ray Photons

X-ray photons are high-energy electromagnetic radiation, and their energy can be calculated using the formula E = hf, where E is energy, h is Planck's constant, and f is the frequency of the radiation. For an X-ray source with an energy of 8 keV, this corresponds to a specific energy value in joules. Knowing the energy of X-ray photons allows for a direct comparison with the energy released during the combustion of methane.

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