# Writing the 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:

$\pu{1.0 M}$ $\ce{NH_3(aq)}$ mixed with $\pu{0.1 M}$ $\ce{BaCl_2(aq)}$ yielded no precipitate when $\pu{1ml}$ of each were mixed together. My unbalanced chemical equation so far looks like:

$$\ce{N^{-3}H3+(aq) + (1/10)Ba^{+2}Cl2-(aq) -> N^{-3}Ba^{+2} + Cl^{-2}H+}$$

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 $\ce{NH}$ is not soluble, but the other compound I think is, which would contradict my observations. Either way, I am incredibly lost.