Problem 95 - General Chemistry: Principles and Modern Applications

Question

Briefly describe (a) the law of conservation of mass (b) Rutherford's nuclear atom (c) weighted-average atomic mass (d) a mass spectrum

Step-by-Step Solution

Answer

(a) The law of conservation of mass states that matter cannot be created nor destroyed in an isolated system. (b) Rutherford's nuclear atom model describes an atom with a centralized nucleus and electrons orbiting around it. (c) The weighted-average atomic mass is calculated by taking into account the relative abundance of different isotopes of an element. (d) A mass spectrum is a graph representing the distribution of ions by their mass-to-charge ratio.

Step 1: Define the Law of Conservation of Mass

The law of conservation of mass states that matter cannot be created nor destroyed in an isolated system. In other words, the total amount of mass remains constant in any system that does not have matter or energy added or removed.

Step 2: Explain Rutherford's Nuclear Atom

Rutherford's nuclear atom concept refers to a model in which an atom's mass and positive charge are concentrated in a central core, called the nucleus. The rest of the atom is mostly empty space, with electrons orbiting around the nucleus.

Step 3: Detail the Weighted-Average Atomic Mass

The weighted-average atomic mass is a calculation method that takes into account the relative abundance of different isotopes of an element. It is calculated by multiplying the atomic mass of each isotope by its relative abundance (in decimal form), and then summing these values.

Step 4: Describe a Mass Spectrum

A mass spectrum is a graph that represents the distribution of ions by their mass-to-charge ratio. It is usually obtained using a mass spectrometer and the information derived from it can give insights into the elemental composition and structural information of a sample.

Key Concepts

Law of Conservation of Mass

The law of conservation of mass is a fundamental principle in chemistry. It tells us that matter cannot be created or destroyed in an isolated system. Imagine you are conducting a chemical reaction in a closed jar. Throughout the reaction, the total mass inside the jar stays constant. This is because, despite possible changes in states or forms, the amount of matter remains unchanged. This principle helps in balancing chemical equations. If we start with a certain amount of reactants, the mass of products must match exactly, ensuring matter is conserved. This understanding not only aids chemical calculations but also reinforces the predictability of chemical processes.

Rutherford's Nuclear Model

Rutherford’s nuclear model revolutionized our understanding of atomic structure. Prior to Rutherford, atoms were believed to be a 'plum pudding' where positive and negative charges were mixed together. However, Rutherford’s famous gold foil experiment led to a new perception. By observing how alpha particles were deflected when shot through a thin piece of gold, Rutherford concluded that atoms have a dense center called the nucleus. This nucleus contains the atom's mass and positive charge. The rest of the atom is mostly empty space, with electrons orbiting around the nucleus. This model is foundational for modern atomic theory, offering insights into atomic behavior, bonding, and reactions.

Weighted-Average Atomic Mass

The concept of weighted-average atomic mass helps in understanding the average mass of an element's atoms. Real elements exist as isotopes, which are versions of an element with different numbers of neutrons. Some isotopes are more abundant than others. The weighted-average atomic mass is calculated by multiplying each isotope's mass by its relative abundance. You sum these values, and the result is the average atomic mass that appears on the periodic table. This method ensures accuracy and reflects real-world natural abundance, aiding chemists in calculations and predictions involving elemental masses.

Mass Spectrum

A mass spectrum is an instrumental analysis tool used to determine the mass-to-charge ratio of ions. Obtained from a mass spectrometer, a mass spectrum provides a graph that displays the components of a sample. Different peaks represent ions with different masses. By analyzing these peaks, scientists can deduce the molecular structure and elemental composition of a compound. This is crucial in fields such as biochemistry and pharmaceuticals, where precise identification of complex molecules is necessary. Mass spectrometry allows for detailed insights, including detecting trace elements and identifying unknown compounds in a mixture.