Question

It takes \(476 \mathrm{~kJ}\) to remove 1 mole of electrons from the atoms at the surface of a solid metal. How much energy (in kJ) does it take to remove a single electron from an atom at the surface of this solid metal?

Short answer

It takes approximately \(7.906\times10^{-22} \mathrm{~kJ}\) to remove a single electron from an atom at the surface of this solid metal.

Step-by-step solution

Recall Avogadro's number

Recall that Avogadro's number is the number of atoms or particles in one mole. Avogadro's number is approximately \(6.022\times10^{23}\) atoms or particles per mole.

Calculate the energy required to remove 1 electron

To find the energy required to remove a single electron from an atom at the surface of this solid metal, we will divide the given energy to remove 1 mole of electrons by Avogadro's number. Let E represent the energy needed to remove a single electron. E = (Energy to remove 1 mole of electrons) / (Avogadro's number) E = \(476\mathrm{~kJ} \div 6.022\times10^{23} \mathrm{~atoms}\)

Calculate the final result

Now, divide 476 kJ by \(6.022\times10^{23}\) atoms to get the energy required to remove a single electron. E = \(\frac{476\mathrm{~kJ}}{6.022\times10^{23}\mathrm{~atoms}}\) E = \(7.906\times10^{-22} \mathrm{~kJ}\) So, it takes approximately \(7.906\times10^{-22} \mathrm{~kJ}\) to remove a single electron from an atom at the surface of this solid metal.

Key concepts

Avogadro's Number

Avogadro's number is a fundamental constant that plays a crucial role in chemistry and physics. It represents the number of constituent particles, usually atoms or molecules, that are contained in one mole of a substance. The mole is a standard unit of measurement in chemistry that is used to express amounts of a chemical substance.

Named after the Italian scientist Amedeo Avogadro, Avogadro's number is defined as approximately \(6.022 \times 10^{23}\) entities per mole. This number was first calculated by Jean Perrin as a way to directly measure the number of molecules in a given volume of gas.

• Application in Calculations: It allows chemists to convert between the mass of a substance and the number of atoms or molecules it contains.
• Quantifies Particles: By relating macroscopic weights to microscopic particles, the mole concept and Avogadro's number bridge the gap between the scale of atoms and our day-to-day measurements.
• Constant Proportion: No matter what substance we are dealing with, one mole of pure substance always contains the same number of particles, thanks to this universal number.

Understanding Avogadro's number is essential when dealing with chemical reactions and the formation of compounds, as it ensures accurate stoichiometric calculations.

Energy Calculation

In physics and chemistry, the concept of energy calculation involves determining the amount of energy associated with a particular process or reaction. Since energy can be neither created nor destroyed (according to the law of conservation of energy), calculations can help predict how energy will transfer or transform from one form to another during a reaction.

For the removal of an electron from the surface of a metal, as illustrated in our exercise, the energy calculation is essential to understanding the energetic costs of electron detachment at the atomic level.

• Quantitative Analysis: It provides a numeric value of energy, often expressed in units like joules (J) or kilojoules (kJ).
• Essential for Processes: From biological systems to technological applications, precise energy calculations are vital. For example, knowing the energy required to remove an electron can inform the energy input needed for a chemical reaction or a physical change such as phase transitions.

By mastering energy calculations, one gains a deeper understanding of chemical bonding, the stability of atoms, and the energy profiles of chemical reactions.

Mole Concept

The mole concept is a method within chemistry for directly relating the mass of substances to the number of particles found within them. It is a cornerstone of the discipline because it facilitates the conversion between mass and the number of atoms, ions, or molecules in a sample.

One mole corresponds to \(6.022 \times 10^{23}\) (Avogadro's number) of particles of the substance. The mole allows scientists to work with quantities large enough to be measured, which can then be translated into workable numbers of molecules.

• Simplicity in Measurement: Instead of counting each individual particle, which is impractical, we measure a substance's weight and infer the number of particles from that weight.
• Universal Unit: The mole is a consistent standard for measurement across all chemical substances.
• Stoichiometry: This concept is essential in stoichiometric calculations, which predict the quantities of reactants and products in chemical reactions.

Understanding the mole concept is critical as it connects the small, invisible particles that make up matter with measurable quantities we can observe in the lab or in industry.