Question

The electrical conductance of copper metal decreases with increasing temperature, but that of a \(\mathrm{CuSO}_{4}\) solution increases with increasing temperature. Explain.

Short answer

Copper's conductance decreases with temperature due to electron scattering, while CuSO4 solution's conductance increases as ion mobility improves.

Step-by-step solution

Understand the properties of copper metal

Copper metal is a good conductor of electricity because it contains free moving electrons. As temperature increases, the atoms in the copper lattice vibrate more vigorously, which scatters the electrons and impedes their flow. This results in a decrease in electrical conductance with increasing temperature.

Understand the properties of a CuSO4 solution

A solution of \(\mathrm{CuSO}_{4}\) conducts electricity through ions instead of free electrons. When temperature increases, the ions in the solution gain more kinetic energy, which increases their mobility and hence enhances the electrical conductance.

Compare the mechanisms of conduction

Copper metal conducts electricity through electron flow, while \(\mathrm{CuSO}_{4}\) solution conducts electricity through ion flow. Increased temperatures cause more lattice vibration in copper obstructing electrons, whereas in a solution, increased temperature enhances ion mobility, thus increasing conductance.

Key concepts

Copper Metal

Copper metal is widely renowned for its excellent electrical conductivity. This is achieved through the movement of free electrons within its atomic structure.
The atoms in copper form a lattice, a repetitive three-dimensional arrangement that allows electrons to flow easily.

• As temperature rises, this lattice vibrates more.
• These vibrations cause greater scattering of the conduction electrons, making it harder for them to move uniformly.
• This results in a decrease in the metal's electrical conductance.

Therefore, copper's conductance is inversely related to temperature.

CuSO4 Solution

The behavior of a \(\mathrm{CuSO}_{4}\) solution involves conducting electricity through ions, unlike copper, which uses free electrons.
In a liquid solution, ions such as \(\text{Cu}^{2+}\) and \(\text{SO}_4^{2-}\) are the carriers of electric current.

• When the temperature increases, ions gain kinetic energy.
• This increment in energy boosts their mobility within the solution.
• As a result, the solution becomes more conductive with temperature rise.

This heightened ion mobility in \(\mathrm{CuSO}_{4}\) accounts for the increase in electrical conductance with temperature.

Temperature Dependence

The dependence on temperature of electrical conductivity varies between substances. In copper metal, higher temperatures disrupt the electron flow because of increased vibrations within the copper lattice.
This leads to reduced electrical conductance.
Meanwhile, \(\mathrm{CuSO}_{4}\) solutions react differently.

• The ions in the solution move more vigorously with increased temperature, hence enhancing conduction.
• This makes the solution's conductance directly proportional to temperature.

Understanding this variance is key to comprehending electrical conductance in different materials.

Electron Mobility

Electron mobility refers to how quickly and efficiently electrons move within a conductor like copper metal.
High mobility indicates fewer obstacles for electrons.

• In copper, electrons are free-moving but can be scattered by atomic vibrations from heat.
• This scattering reduces mobility at higher temperatures, decreasing conductance.
• The direct relationship between temperature and electron scattering is essential to consider for copper's conduction efficiency.

This critical concept explains why conductance drops as copper heats up.

Ion Mobility

Ion mobility is a crucial factor for solutions such as \(\mathrm{CuSO}_{4}\).
Unlike electrons in metals, ions in a solution gain speed with temperature, enhancing their flow.

• Increasing temperature boosts ion energy, facilitating faster movement.
• This increased mobility allows freer passage of electricity through the solution.
• Thus, conductance in a \(\mathrm{CuSO}_{4}\) solution rises with a temperature increase due to enhanced ion mobility.

Knowing this concept aids in understanding why solutions demonstrate improved conductivity at higher temperatures.