How to convert micromolar concentrations into molar quantities, when the volume is also known \begin{array}{c|cccccc}
\text{Sample} &amp; \text{Ammonia} &amp; \text{Phosphate} &amp; \text{Silicate} &amp;\text{Nitrate + nitrite} &amp; \text{Nitrite} &amp; \text{Mn} \\
 &amp; (\pu{\mu M}) &amp; (\pu{\mu M}) &amp; (\pu{\mu M}) &amp; (\pu{\mu M}) &amp; (\pu{\mu M}) &amp; (\pu{\mu g L-1}) \\
\hline
\text{Water} &amp; 0.02 &amp; 0.51 &amp; 9.92 &amp; 9.93 &amp; 0.00 &amp; 0.2 \\
\text{Core 1} &amp; 189.74 &amp; 6.13 &amp; 24.56 &amp; 0.73 &amp; 0.73 &amp; 320.2
\end{array}

The samples are from sediment cores. Different cores have different volume; I need to work in quantities rather than concentrations. I need to calculate the mole (actually micromole) quantities of the $\ce{Mn}$, $\ce{NH3}$, $\ce{NO3-}$ and $\ce{NO2-}$ from their concentrations. The volume for core 1 that is provided here is $\pu{6.86 L}$.

Perhaps I'm being silly, but I am not sure how to do this and how to present this data that is to plotted as follows: molar quantities of the nutrients and metals ($y$-axis) against the oxygen molar concentration ($\pu{\mu M}$) of the water ($x$-axis).

I am also supposed to explain the results in terms of redox chemistry and try to determine approximately at what oxygen concentration in the overlying water these redox reactions in the underlying sediment are initiated.
Molar concentration, or molarity, is moles per unit volume. If you know concentration and sample volume, you can calculate the moles of a particular component in the sample. Since your concentrations are already in micro-molar, when you multiply by the sample volume (in liters), you will have the micro-moles of each component. 

For the Mn result, you will get the mass of Mn (in micrograms) when you multiply the test result by the sample volume, so you can convert that to moles using the molar mass of Mn.