Question

A student designs an ammeter (a device that measures electrical current) that is based on the electrolysis of water into hydrogen and oxygen gases. When electrical current of unknown magnitude is run through the device for 2.00 min , 14.7 mL of water-saturated H2(g) is collected. The temperature and pressure of the system are 25 ∘C and 715 torr.

How many moles of hydrogen gas are produced? 5.47*10^-4 mol

Calculate the magnitude of the current in amperes if the number of moles of hydrogen gas produced is 5.47×10⁻⁴ mol (from part A).

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Answer 1

Given that the moles of H2 gas = 5.47×10⁻⁴ mol

I = Q/t,

here I is current, Q is total charge passing, and t is time for total charge to pass.

the electrolysis of water into hydrogen and oxygen gases is following:

2H2O(l) --> O2(g) + 4H+ + 4e-
4H+ + 4e- --> 2H2(g)

2H2O(l) --> 2H2(g) + O2(g)

n = 5.47×10⁻⁴ mol
This is the amount of moles of water oxidized. Convert this number to the number of moles of electrons produced.

5.47×10⁻⁴ mol H2O * 4mol electrons/2mol H2O = 1.09*10^-3 mol electrons

Convert this number to total charge by using Avogadro’s number and the amount of charge per electron.

1.09*10^-3 electrons * 6.022*10^23 electrons/1mol electrons * 1.602*10^-19 C/1 electron

= 105.15 C

This is the total charge passing through the cross section. Find the current by using the first equation.

Here time t= 2 min

I = 105.15 C/ 2 .00min = 52.6 C/min

Convert this number to amperes.

52.6 C/min * 1min/60s * 1A/(1C/s) = 0. 88 A

The magnitude of the electrical current is 0. 88 A.