When 482,500 coulombs are passed through water, how many moles of hydrogen gas are formed?

To determine how many moles of hydrogen gas are produced when a specific amount of electric charge is passed through water, one must use Faraday's laws of electrolysis. When water undergoes electrolysis, it splits into hydrogen and oxygen gases. The reaction can be summarized by the half-reaction for hydrogen:

[ 2H^+ + 2e^- \rightarrow H_2(g) ]

This equation shows that 2 moles of electrons are required to produce 1 mole of hydrogen gas.

To relate the charge in coulombs to moles of electrons, Faraday's constant, which is approximately 96485 coulombs per mole of electrons, comes into play. This constant indicates that 96485 coulombs are needed to transfer one mole of electrons.

Given that 482,500 coulombs are passed through water, we can first find out how many moles of electrons this represents:

[ \text{Moles of electrons} = \frac{\text{Total charge}}{\text{Faraday's constant}} = \frac{482,500 \text{ C}}{96485 \text{ C/mol}} \approx 5 \text{ mol} ]

Since two moles of electrons are required