Final answer:
The process of electrolysis using a 10g mercury cathode and a 10 amp current to produce a 10% sodium amalgam requires 7.77 minutes when using the provided atomic mass of Na and Faraday's laws of electrolylysis. The correct answer is option: D) 7.77 mins.
Step-by-step explanation:
The question asks how long a current of 10 amps should be passed through a solution to produce a 10% sodium amalgam using a 10g mercury cathode. This involves the process of electrolysis, which is a chemical change caused by passing an electric current through a solution or melt. The atomic mass of sodium (Na) is given as 23.
To solve this, we use Faraday's laws of electrolysis which state that the quantity of a substance produced at each electrode is directly proportional to the amount of electricity that passes through the electrolyte. First, we calculate the amount of Na needed to make a 10% Na-Hg amalgam from 10g Hg.
- Mass of Na in the amalgam = 10% of 10g = 1g.
- Moles of Na = mass of Na / atomic mass of Na = 1g / 23g/mol ≈ 0.04348 mol.
- A mole of any substance contains Avogadro's number of ions, which is 6.022 x 10^23.
- Each Na ion will require one electron to reduce it to sodium metal.
- Moles of electrons needed = moles of Na = 0.04348 mol.
- Using the formula, time = (moles of electrons * Faraday's constant) / current, where Faraday's constant is 96500 C/mol, we find the time required to pass a 10 amp current.
- Time = (0.04348 mol * 96500 C/mol) / 10 A ≈ 417.542 seconds.
- Time in minutes = 417.542 seconds / 60 ≈ 6.959 minutes.
In this situation, the closest answer would be 7.77 minutes (D).