This question tests understanding of Graham's Law of Diffusion, which describes the relationship between the rate of diffusion of a gas and its molecular properties. We need to recall the mathematical formulation of this law.
Graham's Law of Diffusion: This law states that the rate of diffusion or effusion of a gas is inversely proportional to the square root of its molar mass (or molecular weight) at constant temperature and pressure.
The mathematical expression for Graham's Law is:
\[ \text{Rate} \propto \frac{1}{\sqrt{M}} \]where \(\text{Rate}\) is the rate of diffusion/effusion and \(M\) is the molar mass of the gas.
Relating Molar Mass to Density: For an ideal gas, the molar mass (\(M\)) is directly proportional to its density (\(\rho\)) at constant temperature and pressure. This can be derived from the ideal gas law \(PV = nRT\). Since \(n = \frac{m}{M}\), we have \(PV = \frac{m}{M}RT\). Rearranging gives \(PM = \frac{m}{V}RT\). Since \(\rho = \frac{m}{V}\), we get \(PM = \rho RT\). Therefore, \(M = \frac{\rho RT}{P}\). At constant temperature (\(T\)) and pressure (\(P\)), \(M \propto \rho\).
Substituting Density into Graham's Law: Since \(M \propto \rho\), we can substitute density into the proportionality for Graham's Law:
\[ \text{Rate} \propto \frac{1}{\sqrt{\rho}} \]This means the rate of diffusion of a gas is inversely proportional to the square root of its density.
Correct Option: C) Inversely proportional to the square root of its density
This statement accurately reflects Graham's Law of Diffusion, as the rate of diffusion is inversely proportional to the square root of the gas's density (which is directly proportional to its molar mass).
A) Independent of molar mass — This is incorrect. Graham's law explicitly states that the rate is dependent on molar mass, specifically inversely proportional to its square root.
B) Directly proportional to its density — This is incorrect. The rate is inversely proportional to the square root of its density, not directly proportional to its density.
D) Directly proportional to its molar mass — This is incorrect. The rate is inversely proportional to the square root of its molar mass, not directly proportional to its molar mass.
This question asks about Dalton's Law of Partial Pressures, a fundamental concept in chemistry and physics related to the behavior of gas mixtures. We need to recall the definition of this law to identify the correct statement.
D) The sum of partial pressures of individual gases — This is the precise statement of Dalton's Law of Partial Pressures. It applies to mixtures of non-reacting gases where each gas behaves independently.
The question asks to identify a characteristic property of solids. We need to recall the fundamental properties that distinguish solids from liquids and gases, particularly concerning their shape and volume.
A) Definite shape and definite volume. This accurately describes the characteristic properties of solids. Their constituent particles are closely packed and have strong intermolecular forces, giving them a fixed shape and a fixed volume.
The question asks about the arrangement of constituent particles in a crystalline solid. Understanding the fundamental definition of a crystalline solid is key to answering this question.
B) A regular, repeating three-dimensional pattern. This accurately describes the characteristic arrangement of particles in a crystalline solid. The regularity and repetition in three dimensions are defining features of crystallinity.
The question asks to identify an amorphous solid from the given options. Amorphous solids are characterized by a lack of long-range order in their atomic or molecular structure, unlike crystalline solids which have a highly ordered, repeating arrangement.
D) Glass — Glass is a classic example of an amorphous solid. Its constituent particles (primarily silicon dioxide, \(\text{SiO}_2\), but without a regular crystalline lattice) are arranged randomly, giving it properties like a gradual softening upon heating and isotropic behavior. It lacks a definite melting point and breaks into irregular pieces.
This question tests the fundamental understanding of the properties of amorphous solids, specifically their melting behavior. Amorphous solids differ significantly from crystalline solids in their internal structure, which directly impacts how they transition from solid to liquid.
C) Not sharp; it softens over a range of temperatures — This accurately describes the melting behavior of amorphous solids. Due to their disordered internal structure, they do not have a distinct melting point but rather gradually soften and become less viscous over a range of temperatures.