Molarity of hydrogen gas in standard hydrogen electrode

I am unable to understand the folowing statement of [Wikipedia](https://en.m.wikipedia.org/wiki/Standard_hydrogen_electrode) it is about standard hydrogen electrode :



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> The concentration of both the reduced form and oxidised form is maintained at unity. That implies that the pressure of hydrogen gas is 1 bar. 
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But why if I apply ideal gas equation then I am getting molarity of nearly 0.004M .this is condradiction to the statement in Wikipedia. N/V=P/RT THEREFORE M=N/V~0.004




The [standard hydrogen electrode](https://en.wikipedia.org/wiki/Standard_hydrogen_electrode#Construction) is a "reference electrode." It is supposed to be used with ultra-low currents. 


In operation, hydrogen gas is bubbled through a 1 N acid solution, but there is little hydrogen gas in the solution. In order to get the hydrogen gas to bubble through the solution, a pressure of a bit more than 1 bar must be used. 


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The $[H^+]$ ion concentration is unity, i.e. 1M. What you are obtaining by ideal gas equation is number of moles of Hydrogen gas per unit Volume. 


Hope this helps!


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