Amount Of Hydrogen

There is often uncertainty about the amount of hydrogen produced and whether a special exhaust system is already necessary. In this article, this amount is calculated as an example and then extrapolated accordingly in a table.

1. Calculation of the amount of hydrogen produced at 1 ampere

With a current of 1 ampere, a charge of 1 coulomb (= 1 As) flows through the bath per second:

$$ 1 \text{ Ampere} = \frac{6,24 \times 10^{18} \text{ electrons}}{\text{second}} $$

At the cathode, the following reaction takes place with regard to hydrogen:

$$ 2\text{H}^+ + 2e^- \longrightarrow \text{H}_2\uparrow $$

Each hydrogen molecule requires two electrons. From the formulas above, the number of hydrogen molecules produced per second is:

$$ 1 \text{ Coulomb} \approx 6,24 \times 10^{18} \text{ electrons } \Rightarrow \text { 3,12} \times 10^{18} \: \text{H}_2\text{ molecules} $$

To convert this number of molecules produced each second into volume, we need the relationship between amount of substance and volume. Under standard conditions (which are usually roughly met) the following applies for gases:

$$ 1 \text{ mol} \approx 6,022 \times 10^{23} \text{ particles} $$

and

$$ 1 \text{ mol } \hat{=} \; 22,414 \text{ liters} $$

Using these relationships, the volume produced per hour (1 hour = 3600 seconds) is calculated as follows:

$$ V_{1h} = 1\text{A} \times 3600\text{s} \times \frac{3,12 \times 10^{18}}{6,022 \times 10^{23} \text{As}} \times 22,4 \text{ liters} = 0,418 \text{ liters} $$

As a rule of thumb, one can remember:

A current of 2.5 A for 1 hour produces 1 liter of hydrogen.

The amounts produced are always maximum values. In practice, the efficiency is lower – and therefore so is the amount of hydrogen. At low current levels, the amount of hydrogen produced is quite small and is generated over a longer period (one hour), allowing enough time for it to disperse. In a well-ventilated room, even currents of 30 amperes should not pose a problem. Alternatively, there is always the option of passive venting of the hydrogen (bath lid with nozzle and hose), active extraction using a brushless (spark-free!) fan, or – if the lid is tightly sealed – introducing fresh air, which then carries the hydrogen towards the outlet (this avoids fan contact with hydrogen).

2. Table: Amount of hydrogen produced per time and current

The following table lists the maximum possible amount of hydrogen for common currents:

Current (in A)	Volume H2 (in liters/h)
0.5	0.209
1	0.418
2	0.836
3	1.254
4	1.672
5	2.090
6	2.508
7	2.926
8	3.344
9	3.762
10	4.180
15	6.270
20	8.360
25	10.450
30	12.540
35	14.630
40	16.720
45	18.810
50	20.900
60	25.080
70	29.260
80	33.440
90	37.620
100	41.800