magine the battery is so well made that the electrolyte, housing, and everything else non-electrode is massless. What are the theoretical capacities of each electrode, and for the total cell? Provide answers in units of A∗h/g.
Ti capacity:?
Mn capacity:?
cell capacity:?
To determine the theoretical capacities of each electrode and the total cell in terms of A∗h/g (amp-hours per gram), we need to consider the molar mass and valence of the active components in each electrode.
1. Titanium (Ti) Electrode:
The molar mass of Ti is 47.867 g/mol, and its valence is typically +4 in batteries. The Faraday's constant, F, is approximately 96,485 Coulombs/mol.
To calculate the theoretical capacity of the Ti electrode, we need to consider its valence and the charge associated with each Ti ion.
Ti capacity = (valence * F) / molar mass
Ti capacity = (4 * 96,485 C/mol) / (47.867 g/mol)
Ti capacity ≈ 809.3 A∗h/g
Therefore, the theoretical capacity of the Ti electrode is approximately 809.3 A∗h/g.
2. Manganese (Mn) Electrode:
The molar mass of Mn is 54.94 g/mol, and its valence can vary depending on the specific compound and oxidation state. For simplicity, we'll consider Mn with a valence of +2.
Mn capacity = (valence * F) / molar mass
Mn capacity = (2 * 96,485 C/mol) / (54.94 g/mol)
Mn capacity ≈ 349.8 A∗h/g
Therefore, the theoretical capacity of the Mn electrode is approximately 349.8 A∗h/g.
3. Total Cell Capacity:
To determine the total cell capacity, we need to consider the stoichiometry of the reaction occurring in the battery. Assuming a balanced reaction where x moles of Ti react with y moles of Mn, we can calculate the total cell capacity.
Total cell capacity = (x * Ti capacity) + (y * Mn capacity)
Since the stoichiometry of the reaction is not provided in the question, we cannot calculate the specific total cell capacity without additional information. However, it will be dependent on the number of moles of Ti and Mn involved and their respective capacities.
In summary:
Ti capacity ≈ 809.3 A∗h/g
Mn capacity ≈ 349.8 A∗h/g
Total cell capacity = (x * 809.3 A∗h/g) + (y * 349.8 A∗h/g) [x, y are stoichiometric coefficients]