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Chapter 5: Problem 35

If we have \(6 \times 10^{23}\) molecules, \(^{53}\) and each molecule releases \(1 \mathrm{eV}\) in a chemical reaction, how many kJ (per mole, as it turns out) is this reaction?

Short Answer

Expert verified
Question: Calculate the energy per mole in kJ for a chemical reaction if 1 eV of energy is released per molecule and there are \(6 \times 10^{23}\) molecules. Answer: To calculate the energy per mole in kJ, follow these steps: 1. Convert eV to Joules: 1 eV x 1.602 x 10^{-19} J/eV = 1.602 x 10^{-19} J 2. Calculate total energy released: 1.602 x 10^{-19} J x \(6 \times 10^{23}\) molecules = 96.12 J 3. Determine energy per mole: The total energy released (96.12 J) is equal to the energy per mole 4. Convert Joules to kJ: 96.12 J / 1000 = 0.09612 kJ Thus, the energy per mole in kJ for this reaction is 0.09612 kJ.

Step by step solution

01

Convert eV to Joules

To convert the energy from eV to Joules, we need to use the conversion factor: 1 eV = 1.602 x 10^{-19} Joules. Multiply the given energy (1 eV) per molecule by this conversion factor: Energy per molecule (in Joules) = 1 eV x 1.602 x 10^{-19} J/eV
02

Calculate total energy released

Next, we'll multiply the energy per molecule (in Joules) by the given number of molecules, \(6 \times 10^{23}\): Total energy released = Energy per molecule (in Joules) x \(6 \times 10^{23}\) molecules
03

Determine energy per mole

Since there are \(6 \times 10^{23}\) molecules in a mole (Avogadro's Number), the total energy released is actually the energy per mole.
04

Convert Joules to kJ

To convert the energy per mole from Joules to kJ, divide by 1000: Energy per mole (in kJ) = Total energy released (in Joules) / 1000 Using the calculations in Steps 1-4, you can now substitute the values to find the energy per mole in kJ for this reaction.

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