# Economics of Hydrogen Production

Hydrogen has been proposed as carbon-free alternative fuel to hydrocarbons provided the hydrogen is produced from a carbon-free source e.g. renewable or nuclear electricity

The electrochemistry of producing hydrogen (and oxygen) from water using is well understood. One *FARADAY* (96,485 *COULOMBS*) is required to produce one mole of hydrogen atoms - or half a mole of hydrogen molecules (H_{2}). Therefore an electric current of 1 *AMP* will in 1 *SECOND* produce 0.5/96485 = 5.18E-06 moles H_{2}. Assuming a cell *VOLTAGE* of 1.481V that equates to 3.5E-06 moles H_{2} per W-s; 0.0126 moles H_{2} per W-h; 12.6 moles H_{2} per kW-h; 25.2 *GRAMS* H_{2} per kW-h. As hydrogen has a higher calorific value than natural gas (112 MJ/kg versus 50 MJ/kg) multiply by this ratio (112/50) to get 56.4g natural-gas-equivalent per kilowatt-hour electricity

How does the price of hydrogen produced from by electrolysis compare to the cost of natural gas? For electricity @ 8.8p per kW-h and natural gas @ 4.3p per kW-h, the 25.2 g H_{2} (= 56.4g natural-gas-equivalent) costs 8.8p and the *actual* cost of 56.4g natural gas (2.82 MJ; 2820 kJ; 0.784 kW-h) is 3.4p

In other words hydrogen from electricity costs about 2.6x the equivalent amount of natural gas