Water is electrolyzed by passing a current of 0.500 amps through 1.00 L of 1.00 M Na2SO4 solution for 120 minutes. One gas is collected at the anode and a different gas is collected at the cathode.

a. Write the balanced equation for the cathode half-reaction and Find the number of moles of gas produced at the cathode and calculate the volume in liters it occupies as a dry gas at a pressure of 745 mmHg and 25.0 °C.

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The balanced equation for the cathode half reaction can be written as:

`2 H_2O + 2 e^(-) -> H_2 + 2 OH^(-)`

- In order to get the amount of moles, we should first convert the given current into coulomb.

`0.500 amp * 120 m i n utes * (60 s e conds)/(1 m i n ute) = ` **3,600 C**

- Next, we can get moles of Hydrogen gas using the 1 F = 96485 C

`3,600 C * (1 F)/(96485 C) * (1 mol e H_2)/(2 F) =` **0.018656 moles H2**

- In order to get the volume, we can use the ideal gas equation PV = nRT:

`PV = nRT`

- P = 745/760 = 0.9802 atm
- n = 0.018656 moles
- T = 25 + 273.15 = 298.15
- R = 0.08206 atm-L/mol-K

`V = (nRT)/(P)`

`V = ((0.018656)*(0.08206)*(298.15))/(0.9802)`

V = 0.466 L** -> volume **

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