Avoid using chlorinated water as a carrier for inoculant. Inoculant labels will specify not to use chlorinated water because the chlorine can kill the Bradyrhizobia bacteria that converts nitrogen in air to a plant usable form.  Some folks have likely had success using chlorinated water but there is risk and there is no recourse if there is an inoculant failure. This is especially risky on new ground. If you feel like you have no other choice, make sure you apply a peat-based product in the seed hopper as insurance. With nitrogen prices, try not to have an inoculant failure, most especially on new ground.

I have not looked at chlorine-neutralizing products. But after looking into these (after being asked about them,) there is very little confidence in their ability to protect Bradyrhizobia from chlorine.

Also, do not mix up more inoculant for planting than you can plant that day. If the tank sits over night, my recommendation is that you added more inoculant to the tank before planting.