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Chapter 11: Problem 151

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

Short Answer

Expert verified
The conductivity of copper metal decreases with temperature because the increased thermal vibrations of the metal atoms lead to more collisions with free conducting electrons, impeding their flow. Conversely, in a \(\mathrm{CuSO}_{4}\) solution, increasing temperature speeds up ion movement and decreases solution viscosity, which facilitates faster ion transport and increases conductivity.

Step by step solution

01

Understand Electrical Conductance in Metals

In metals, electrical conductivity is due to the movement of free electrons. As temperature increases, the vibrations of the atoms in the metal lattice also increase. This leads to more frequent collisions between the vibrating atoms and the free electrons, which impedes the flow of these electrons. As a result, electrical conductivity decreases with increasing temperature in metals.
02

Understand Electrical Conductance in Electrolyte Solutions

In electrolyte solutions such as \(\mathrm{CuSO}_{4}\), electrical conduction is due to the movement of ions. An increase in temperature often leads to an increase in the speed of movement of these ions and a decrease in the viscosity of the solution. As more ions can move freely and quickly, this results in an increase in electrical conductivity with increasing temperature in electrolyte solutions.
03

Combine the Two Concepts

In order to explain the differing behavior of copper metal and \(\mathrm{CuSO}_{4}\) solution, we can understand that they have different modes of electrical conduction - electrons in the case of copper and ions in the case of \(\mathrm{CuSO}_{4}\) solution. Their response to temperature changes are based on how the heat affects these different modes of conduction - causing more impediment in metals and facilitating faster transport in electrolytes.

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