Question

Which of the following statements is a scientific theory? (a) The energy in an atomic nucleus is found by \(E=m c^{2}\). (b) There is the same number of molecules in equal volumes of gases. (c) If the temperature of a gas doubles, the pressure doubles. (d) The region surrounding the nucleus of an atom contains electrons.

Short answer

Option (d) is a scientific theory.

Step-by-step solution

Understand the Options

Each statement must be considered as to whether it fits the definition of a scientific theory. A scientific theory is a well-substantiated explanation of an aspect of the natural world that can incorporate laws, hypotheses, and facts.

Analyze Option (a)

The statement 'The energy in an atomic nucleus is found by \(E=mc^2\)' refers to Einstein's mass-energy equivalence formula, which is a scientific equation rather than a theory.

Analyze Option (b)

The statement 'There is the same number of molecules in equal volumes of gases' describes Avogadro's Law, which is also typically considered a law rather than a theory.

Analyze Option (c)

The statement 'If the temperature of a gas doubles, the pressure doubles' is a simplified description of the ideal gas law under certain conditions, and is more of a mathematical relationship or law.

Analyze Option (d)

The statement 'The region surrounding the nucleus of an atom contains electrons' fits with the atomic theory, which is a well-substantiated explanation about the components and structure of the atom, qualifying as a scientific theory.

Key concepts

Atomic Theory

Atomic Theory is a fundamental scientific concept that provides a clear understanding of the structure and behavior of atoms, which are the building blocks of matter. This theory has evolved over centuries as scientists have discovered more about the components and behavior of atoms.

Atomic Theory explains that atoms consist of a central nucleus made up of protons and neutrons, surrounded by electrons in orbitals. These electrons move in specific regions around the nucleus, forming what is known as an electron cloud. The theory also covers the behavior of these electrons during chemical reactions. For example, electrons can be gained, lost, or shared between atoms, leading to the formation of molecules and compounds.

The development of Atomic Theory is a testament to the scientific method, where hypotheses have been proposed, tested, and refined over time. From Democritus's early ideas to Dalton’s atomic model, and later advancements by scientists like Rutherford and Bohr, each step has brought a deeper understanding. This theory is essential in describing chemical reactions, explaining isotopes, and even understanding nuclear energy.

Avogadro's Law

Avogadro's Law is an essential concept in chemistry that deals with the behavior of gases. It states that equal volumes of gases, at the same temperature and pressure, contain the same number of molecules. This law is fundamental for understanding chemical reactions involving gases.

Amedeo Avogadro proposed this law in 1811, which later led to the determination of Avogadro's number. Avogadro’s number is the number of constituent particles (usually atoms or molecules) in one mole of a substance and is approximately \(6.022 \times 10^{23}\).

Avogadro's Law is instrumental in calculations involving the molar volume of gases. For example, at standard temperature and pressure (STP), one mole of any gas occupies about 22.4 liters. This relationship helps chemists calculate the amounts of reactants and products in chemical reactions, especially those in the gaseous state. By using Avogadro's Law, chemists can accurately relate volumes of gases to the amount of substance present, facilitating the prediction and analysis of reaction products.

Ideal Gas Law

The Ideal Gas Law is a cornerstone of physical chemistry and thermodynamics, providing a mathematical model to describe the behavior of gases. This law is expressed as \(PV = nRT\), where:

• \(P\) is the pressure of the gas,
• \(V\) is the volume of the gas,
• \(n\) is the number of moles of gas,
• \(R\) is the universal gas constant,
• \(T\) is the temperature of the gas in Kelvin.

The Ideal Gas Law combines several simpler gas laws, such as Boyle's Law, Charles's Law, and Avogadro's Law, into one comprehensive equation. It is crucial for understanding how gases will behave under different conditions such as changes in temperature, pressure, or volume.

While the Ideal Gas Law is a valuable tool, it's important to note that it is an approximation. Real gases do exhibit deviations from ideal behavior, especially under high pressure and low temperature conditions. In these cases, other models like the Van der Waals equation may be more accurate.

In practical applications, the Ideal Gas Law is used in a wide range of scientific and engineering calculations, from determining the composition of planetary atmospheres to designing chemical reactors. It is vital for predicting the behavior of gases in various scientific experiments and industrial processes.