Lake Cayuga has a volume of water estimated to be 8.2*10¹² litres. A power station not so far above Cayuga’s water produces electricity at a rate of 1.5*10⁶ coulomb per second at an appropriate voltage. How long would it take to electrolyse the lake?

To determine how long it would take to electrolyze Lake Cayuga, we first need to understand the process of electrolysis and how it relates to the volume of water and the rate of electricity produced by the power station. Electrolysis involves splitting water (H2O) into hydrogen and oxygen using electrical energy. The key factors here are the volume of water in the lake and the rate at which the power station can provide electrical charge.

Understanding Electrolysis

Water consists of two hydrogen atoms and one oxygen atom. The electrolysis of water requires a certain amount of electrical charge to break these bonds. The reaction can be summarized as follows:

• 2 H2O(l) → 2 H2(g) + O2(g)

To electrolyze 1 mole of water (approximately 18 grams), it requires about 2 Faradays of charge, which is equivalent to 192,000 coulombs. This means that for every mole of water, we need 192,000 coulombs to complete the electrolysis.

Calculating the Volume of Water in Moles

First, we need to convert the volume of Lake Cayuga from liters to moles. Given that the volume of the lake is 8.2 x 10¹² liters, we can calculate the number of moles of water:

• 1 mole of water = 18 grams = 18 mL (since the density of water is approximately 1 g/mL)
• Thus, 8.2 x 10¹² liters = 8.2 x 10¹⁵ mL
• Number of moles = (8.2 x 10¹⁵ mL) / (18 mL/mole) = 4.56 x 10¹⁴ moles

Determining Total Charge Required

Next, we calculate the total charge needed to electrolyze the entire lake:

• Total charge = Number of moles x Charge per mole
• Total charge = (4.56 x 10¹⁴ moles) x (192,000 coulombs/mole) = 8.76 x 10¹⁹ coulombs

Calculating Time for Electrolysis

Now that we know the total charge required, we can find out how long it would take to electrolyze the lake using the power station's output:

• Power station output = 1.5 x 10⁶ coulombs/second
• Time = Total charge / Power station output
• Time = (8.76 x 10¹⁹ coulombs) / (1.5 x 10⁶ coulombs/second) = 5.84 x 10¹³ seconds

Converting Time into More Understandable Units

To make this number more relatable, let's convert seconds into years:

• Seconds in a year = 60 seconds/minute x 60 minutes/hour x 24 hours/day x 365 days/year = 31,536,000 seconds/year
• Time in years = (5.84 x 10¹³ seconds) / (31,536,000 seconds/year) ≈ 1.85 x 10⁶ years

In summary, it would take approximately 1.85 million years to electrolyze Lake Cayuga at the given rate of electricity production. This illustrates not only the vast volume of water in the lake but also the significant amount of energy required for such a process.