# Writing Chemical equation given molarity

If I am given the molarity of two substances and I know how they react, how can I write the balanced chemical reaction? I.e.,

Experimentally I found:

1.0 M $NH_3$(aq) mixed with 0.1 M $BaCl_2(aq)$ yielded NO precipitate when 1ml of each were mixed together. My unbalanced chemical equation so far looks like

$\ce{N^{-3}H^+_3(aq) + (1/10)Ba^{+2}Cl^-_2(aq) -> N^{-3}Ba^{+2} + Cl^{-2}H^+}$

My logic being: since the solutions are administered in equal volumes, their molarity determines the molar coefficients. Right off the bat I can tell that NH is NOT soluble, but the other compound I think is, which would contradict my observations. Either way, I am incredibly lost. Any help greatly appreciated.

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