Cesium metal is produced by the electrolysis of molten cesium cyanide. Calculate the maximum amount of Cs(s) that can be deposited from CsCN(l) in 30.0 minutes by a current of 500.0 mA Answer is given as 1.24 g. Unsure of how to solve for it. thank you!
The Correct Answer and Explanation is:
The correct answer is 1.24 g of Cesium.
This problem is solved using the principles of stoichiometry and Faraday’s laws of electrolysis, which link the amount of electric current passed through a substance to the amount of chemical change that occurs. The process involves several key steps.
First, you must determine the relevant chemical reaction. In the electrolysis of molten cesium cyanide (CsCN), cesium ions (Cs⁺) are reduced at the cathode to form solid cesium metal. The balanced reduction half-reaction is:
Cs⁺(l) + 1 e⁻ → Cs(s)
This equation is crucial because it shows that one mole of electrons (e⁻) is required to produce one mole of solid cesium (Cs).
Next, you need to calculate the total electric charge passed through the solution. First, convert the given values into standard SI units. The time is 30.0 minutes, which is 1800 seconds (30.0 min × 60 s/min). The current is 500.0 milliamperes (mA), which is 0.5000 amperes (A) or Coulombs per second (C/s). The total charge (Q) is calculated by multiplying the current (I) by the time (t):
Q = I × t = 0.5000 C/s × 1800 s = 900.0 Coulombs
Now, you convert the total charge into moles of electrons using the Faraday constant (F), which is approximately 96,485 Coulombs per mole of electrons.
Moles of electrons = Q / F = 900.0 C / 96,485 C/mol e⁻ ≈ 0.009328 moles of electrons
Based on the 1:1 molar ratio from our half-reaction, the moles of cesium produced are equal to the moles of electrons.
Moles of Cs = 0.009328 mol
Finally, convert the moles of cesium to mass using its molar mass (132.91 g/mol ).
Mass of Cs = moles × molar mass = 0.009328 mol × 132.91 g/mol ≈ 1.2395 g
Rounding to three significant figures (from 30.0 minutes), the final answer is 1.24 g.
