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 4.00 min, 13.8 mL of water-saturated H2 (g) is collected. The temperature and pressure of the system are 25 ∘C and 715 torr.

Here we will find the amount of current required for the electrolysis of water as follows:

PV = nRT ... ideal gas

n = PV / (RT)

where

P = 715 Torr = 715 x 0.133kPa = 95.3kpa

T=25 ∘C = 298k

V = 13.8 mL = 13.8 x 10⁻⁶m³

R=8.314J/mol. k

No. of moles of H₂, n = 95.3 * 10³ x 13.8 x 10⁻⁶ / (8.314 * 298) = 5.31 * 10⁻⁴ mol

To produce H₂ gas, we have the reaction,

2H⁺ (aq) + 2e⁻ → H₂ (g)

According to the equation above, the production of 1 mole of H₂ needs 2moles of electron, e⁻.

Number of moles of e⁻ = (5.31 * 10⁻⁴) * 2 = 1.06 * 10⁻³ mol

Each molecules of e⁻ carries 96500 C of electricity.

Amount of electricity, Q = 96500 * (1.06 * 10⁻³) = 102.47 C

Q = It

Current, I = Q/t = 102.47 / (4 * 60) = 0.426 A