Problem 73 - Chemistry The Central Science

Question

(a) What happens to the emf of a battery as it is used? Why does this happen? (b) The AA-size and D-size alkaline batteries are both \(1.5-\mathrm{V}\) batteries that are based on the same electrode reactions. What is the major difference between the two batteries? What performance feature is most affected by this difference?

Step-by-Step Solution

Answer

(a) As a battery is used, its emf (electromotive force) gradually decreases. This occurs due to the decrease in the concentration of ions in the electrolyte and buildup of product ions, which create an internal resistance that opposes the flow of electrons. (b) The major difference between AA-size and D-size alkaline batteries, both providing 1.5 V, is their size and capacity. D-size batteries have a larger size, which allows them to store more energy in the form of chemical reactants. The performance feature most affected by this difference is the battery life. D-size batteries have a longer battery life and higher energy capacity compared to AA-size batteries due to their increased size and storage capacity.

Step 1: Understanding emf changes in a battery as it is used

Emf, or electromotive force, is the energy provided by a cell or battery per unit charge that flows through it. As a battery is used, its emf gradually decreases. This mainly happens because of the decrease in the concentration of ions in the electrolyte and buildup of the product ions that create an internal resistance within the battery. This internal resistance opposes the flow of electrons, causing a decrease in the emf.

Step 2: Identifying the major difference between AA-size and D-size batteries

Both AA-size and D-size alkaline batteries provide the same voltage (1.5 V) and are based on the same electrode reactions. The major difference between them lies in their size and capacity. D-size batteries are larger than AA-size batteries, allowing them to store more energy in the form of chemical reactants.

Step 3: Describing the performance feature most affected by the difference

The performance feature most affected by the size difference between AA-size and D-size batteries is the battery life. As the capacity of a D-size battery is higher compared to that of an AA-size battery, it can deliver the same amount of power at a constant voltage for a longer time before being fully discharged. In other words, D-size batteries have a longer battery life and higher energy capacity compared to AA-size batteries due to their increased size and storage capacity.

Key Concepts

Battery voltage

Battery voltage is a key concept when understanding how batteries work. The voltage of a battery is essentially the electrical potential difference between its terminals. For AA-size and D-size batteries, the voltage is always 1.5 volts. This voltage is determined by the materials and chemical reactions inside the battery, which create a flow of electrons.

Voltage is important because it's the driving force that moves electrons through a circuit. It determines how much energy per charge is available to do work. However, even though AA and D-size batteries have the same voltage, their sizes result in different performance characteristics.

Internal resistance

Internal resistance is a significant factor that influences the performance of a battery. It refers to the opposition within the battery to the flow of current. This resistance is caused by the materials comprising the battery, including the electrolyte and the electrodes.

As a battery discharges, internal resistance can increase due to several factors. These include the buildup of products from chemical reactions and decreased ion concentration. As the resistance increases, it becomes harder for the current to flow, resulting in decreased efficiency and reduced potential output voltage.

Battery capacity

Battery capacity refers to the amount of energy a battery can store and deliver. It is measured in ampere-hours (Ah) and depends on the size and design of the battery. While voltage is the same in AA and D-size batteries, capacity can differ significantly.

A D-size battery has a higher capacity than an AA battery because it can hold more active chemical material. This results in more energy being stored, allowing the battery to operate for a longer period before needing replacement or recharging. Capacity is crucial for devices that require long lasting power outputs, such as flashlights and radios.

Battery life

Battery life is closely related to battery capacity but refers specifically to how long a battery can power a device before it is empty. While both AA and D batteries share the same voltage, the larger capacity of D-size batteries allows them to last longer.

Factors influencing battery life include device power consumption and the efficiencies of the chemical reactions inside the battery. A battery with higher capacity will generally result in a longer battery life, making it more suitable for high-drain devices or prolonged usage situations.

Ultimately, understanding these factors helps consumers select the right battery type for their needs, ensuring their devices operate efficiently and for the desired duration.