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 maximum amount of Cesium (Cs) that can be deposited is 1.24 grams.
This calculation is a direct application of Faraday’s laws of electrolysis, which connect the amount of electrical charge passed through a solution to the amount of chemical change that occurs. The process involves a series of conversions from electrical units to chemical quantities.
First, we must determine the total electrical charge (Q) that passed through the molten cesium cyanide. The formula for charge is Q = I × t, where I is the current in amperes (A) and t is the time in seconds (s). We need to convert the given values into these standard units. The current is 500.0 milliamperes (mA), which is 0.5000 amperes (A). The time is 30.0 minutes, which is equivalent to 1800 seconds (30.0 min × 60 s/min).
Calculating the charge:
Q = 0.5000 A × 1800 s = 900.0 Coulombs (C).
Next, we use Faraday’s constant (F), which is approximately 96,485 Coulombs per mole of electrons (C/mol e⁻), to find out how many moles of electrons this charge represents.
Moles of electrons = Total Charge / Faraday’s Constant
Moles of electrons = 900.0 C / 96,485 C/mol e⁻ ≈ 0.009328 mol e⁻.
The production of solid cesium from molten cesium cyanide involves the reduction of cesium ions (Cs⁺) at the cathode. The balanced half-reaction for this process is:
Cs⁺ + 1e⁻ → Cs(s)
This equation shows a crucial one to one molar ratio: one mole of electrons is required to produce one mole of solid cesium. Therefore, the moles of cesium produced are equal to the moles of electrons calculated.
Moles of Cs = 0.009328 mol.
Finally, to find the mass of cesium deposited, we multiply the moles of cesium by its molar mass, which is 132.91 g/mol .
Mass of Cs = 0.009328 mol × 132.91 g/mol ≈ 1.2395 g.
Rounding to three significant figures, based on the 30.0 minutes given in the problem, the final answer is 1.24 grams
