🔋 Battery Chemistry

From Ions to Electrons: Understanding AA Alkaline Batteries

How Batteries Work

When you insert AA batteries into your RC car controller or the car itself, you're using electrochemistry to convert chemical energy into electrical energy. Inside an alkaline battery, a redox reaction occurs between zinc metal and manganese dioxide.

The Alkaline Cell Reaction

An alkaline battery produces electricity through a redox reaction, which is a process involving the transfer of electrons from an anode to a cathode through an external circuit. The name "alkaline" comes from the electrolyte used: potassium hydroxide (KOH), which provides a very basic (alkaline) environment for the ions to move.

Oxidation at the Anode (Negative Terminal)

At the negative terminal, zinc metal (Zn) is oxidized. It reacts with hydroxide ions (OH⁻) from the electrolyte, releasing electrons and forming zinc oxide:

Zn(s) + 2OH⁻(aq)  → ZnO(s) + H₂O(l) + 2e⁻

What this means: Zinc atoms give up two electrons each. These electrons are pushed out of the battery and flow through your device (like an RC car motor).

Reduction at the Cathode (Positive Terminal)

At the positive terminal, reduction occurs. Manganese dioxide (MnO₂) accepts the electrons from the circuit and reacts with water to form manganese(III) oxide:

2MnO₂(s) + H₂O(l) + 2e⁻ → Mn₂O₃(s) + 2OH⁻(aq)

What this means: The manganese dioxide acts as a sink for the electrons. By absorbing them, it changes its chemical structure into manganese(III) oxide and releases hydroxide ions back into the electrolyte to keep the cycle going.

Overall Net Reaction

When the two half-reactions are combined, the water and hydroxide ions cancel out, leaving the total chemical change:

Zn(s) + 2MnO₂(s) → ZnO(s) + Mn₂O₃(s)

Key Technical Facts

Electrolyte Role: The Potassium Hydroxide (KOH) electrolyte is not consumed during the reaction. Instead, it acts as a shuttle, allowing hydroxide ions (OH⁻) to travel between the cathode and anode to maintain a closed circuit.
Stoichiometry: For every 1 mole of zinc oxidized at the anode, 2 moles of electrons are released into the circuit. This 1:2 ratio is used to calculate the battery's total capacity and runtime.
Nominal Voltage: The chemical potential difference between Zinc and Manganese Dioxide produces a nominal voltage (standard voltage level) of 1.5V per cell. It starts slightly higher (around 1.6V), and gradually decreases as the chemical reactants are converted into products.
Shelf Life: Because the zinc is in powder form and the electrolyte is stable, alkaline cells can hold their charge for 5-10 years.

The actual alkaline cell chemistry is more complex. The cathode reaction can go through multiple steps, and the products depend on discharge rate and depth. The simplified equation above represents the net effect of the reaction.

In reality, the electrolyte is concentrated potassium hydroxide, and intermediate compounds form during discharge. For our calculations, the simplified reaction with 2 electrons per zinc atom is a reliable approximation used for calculating battery capacity and performance.

⚡ Electron Flow Visualization

🔋

Anode (−)

⚡

Motor

Electrons flow from the negative terminal (anode) through the external circuit to power the motor, then return to the positive terminal (cathode).

💡 Did You Know?

🌍 Battery Production

Over 15 billion AA batteries are produced worldwide each year! That's about 2 batteries for every person on Earth.

⏰ The First Battery

Alessandro Volta invented the first true battery (the "voltaic pile") in 1800. The unit of electric potential, the volt, is named after him!

🦎 Zinc in Nature

Zinc, the anode material in alkaline batteries, is essential for life! It's found in every cell of your body and helps your immune system function.

♻️ Recycling Benefits

A single recycled alkaline battery can save enough energy to power a TV for 3 hours. The zinc and manganese can be reused in new products!

Putting Chemistry to Work

Now that you understand the chemical reactions inside a battery, let's calculate exactly how much energy your batteries can provide. This is important for understanding how long your RC car can run and how fast it can go.

Why These Calculations Matter

When choosing batteries for your RC car, you need to answer important questions:

How long will my car run? — The calculator converts battery capacity (measured in milliamp-hours) into total energy (joules) and runtime estimates
How much power can be delivered? — Higher current = faster motor, but also faster battery drain and more voltage drop
Alkaline vs. Rechargeable Nickel-Metal Hydride (NiMH)? — NiMH batteries have lower voltage (1.2V vs 1.5V) but can deliver higher currents with less voltage sag
What's the limiting factor? — Using stoichiometry, we can calculate how much charge the chemical reaction can actually produce

Try the calculator below with different battery configurations to see how they affect your RC car's performance!

🧮 Battery Calculator

Calculation Mode

Cell Voltage (V)

Cells in Series

Cells in Parallel

Internal Resistance: 0.3 Ω Affects loaded voltage when current flows

Motor Current Draw (A) - for runtime estimate

Results

Pack Voltage: 1.50 V

Loaded Voltage: — V

Total Charge (Q): 7200.00 C

Capacity: 2000 mAh

Energy: 10800.00 J

Energy (Wh): 3.00 Wh

Est. Runtime: — min

Limiting Reactant: —

Select "Stoichiometry" mode and adjust inputs to see step-by-step calculations.

📐 Key Formulas

Moles from Mass

n = m / M

n = moles, m = mass (g), M = molar mass (g/mol)

What it does: Converts the physical amount of a substance (grams) to the chemical amount (moles). This is essential because chemical equations work with moles, not grams.

Example: 65.38 g of Zn = 1 mole of Zn atoms (about 6 × 10²³ atoms!)

Charge from Moles

Q = n × F

Q = charge (C), n = moles of electrons, F = 96,485 C/mol

What it does: Tells us how much electric charge is carried by a given number of electrons. The Faraday constant (F) is the charge of one mole of electrons.

Why it matters: This links chemistry (moles) to electricity (Coulombs), and is important for calculating battery capacity.

Energy from Charge

E = V × Q

E = energy (J), V = voltage (V), Q = charge (C)

What it does: Calculates the total energy available from a battery. Voltage is the "push" per unit charge, so multiplying by total charge gives total energy.

Real-world use: Compare batteries: a 1.5V AA has less energy than a 9V battery with the same charge capacity.

Capacity Conversion

Q (C) = mAh × 3.6

1 mAh = 0.001 Ah = 3.6 C

What it does: Converts manufacturer ratings (mAh) into the standard physics unit for charge (Coulombs).

Why 3.6?: Since 1 Amp is 1 Coulomb per second, and there are 3,600 seconds in an hour, multiplying milliamp-hours by 3.6 (which is 3600 / 1000) gives you the exact charge in Coulombs.

Nickel-Metal Hydride (NiMH) Chemistry

NiMH batteries have a different chemistry than alkaline cells. The anode uses a hydrogen-absorbing metal alloy (MH), and the cathode uses nickel oxyhydroxide (NiOOH).

Simplified Reactions:

Anode: MH + OH⁻ → M + H₂O + e⁻
Cathode: NiOOH + H₂O + e⁻ → Ni(OH)₂ + OH⁻

Key differences from alkaline:

Lower nominal voltage: 1.2 V (vs 1.5 V for alkaline)
Rechargeable (typically 500-1000 cycles)
Lower internal resistance
Flatter discharge curve (voltage stays more constant)

📖 Worked Examples

Example 1: Single AA Battery Energy

Problem: A typical AA alkaline battery has a capacity of 2000 mAh at 1.5 V. Calculate the total energy in Joules and Watt-hours.

Step 1: Convert capacity to Coulombs

Q = 2000 mAh × 3.6 = 7200 C

Step 2: Calculate energy in Joules

E = V × Q = 1.5 V × 7200 C = 10,800 J

Step 3: Convert to Watt-hours

E = 10,800 J ÷ 3600 = 3.0 Wh

Answer: 10,800 J or 3.0 Wh

Example 2: 4×AA Pack for RC Car

Problem: An RC car uses 4 AA batteries in series. If each cell is 1.5 V with 2000 mAh, what is the pack voltage and energy available? If the motor draws 0.5 A, estimate the runtime.

Step 1: Pack voltage (series adds voltage)

V_pack = 4 × 1.5 V = 6.0 V

Step 2: Pack capacity (series keeps same capacity)

Capacity = 2000 mAh (unchanged in series)

Step 3: Total energy

E = V × Q = 6.0 V × 7200 C = 43,200 J = 12.0 Wh

Step 4: Runtime estimate

Runtime = 2000 mAh ÷ 500 mA = 4.0 hours

Answer: 6.0 V pack, 12.0 Wh, approximately 4 hours runtime at 0.5 A draw.

Example 3: Stoichiometry Calculation

Problem: Calculate the theoretical charge from a reaction of 1.0 g Zn with 2.0 g MnO₂.

Step 1: Calculate moles

n(Zn) = 1.0 g ÷ 65.38 g/mol = 0.01530 mol
n(MnO₂) = 2.0 g ÷ 86.936 g/mol = 0.02301 mol

Step 2: Find limiting reactant (ratio 1:2)

Zn needed for all MnO₂: 0.02301 ÷ 2 = 0.01150 mol
Available Zn: 0.01530 mol
Since 0.01530 > 0.01150, MnO₂ is limiting

Step 3: Calculate electrons (2 per reaction)

n(e⁻) = 0.01150 × 2 = 0.02301 mol

Step 4: Calculate charge

Q = n × F = 0.02301 × 96485 = 2220 C

Answer: MnO₂ is limiting; theoretical charge = 2220 C

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