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If you mix $\pu{20 ml}$ of $\pu{3 M}$ sugar solution with $\pu{30 ml}$ of a $\pu{5 M}$ sugar solution, what solution do you end up with?
What I did,
\begin{align} \text{volume} &= \frac{\text{amount of substance}}{\text{concentration}}\\ \dfrac{3}{0.02} &= 150\\ \dfrac{5}{0.03} &= 166.\overline{6}\\ 150+166.\overline{6} &= 316.\overline{6} \end{align}
This is the wrong answer. Any formulas which could help would be appreciated.
3M and 5M mean 3 mol/L and 5 mol/L i.e. the concentration. 20ml and 30ml are the volume. You said you were calculating the volume but you actually divided the concentration by the volume which gives mol/L/L. And you don't need to calculate any volumes since they are given, and you can add them to get the final volume. They want you to use this to find the final concentration.
Remember two solutions of different concentrations are mixed together, the total amount of substance of the solution is the sum of the amounts of the individual solutions. when you get the sum of the amounts, you add their volumes and use those two to determine the new concentration of the solution. $$n_1=0.02\ \mathrm l\times3\ \mathrm{mol\ l^{-1}}=0.06\ \mathrm{mol}$$ $$n_2=0.03\ \mathrm l\times5\ \mathrm{mol\ l^{-1}}=0.15\ \mathrm{mol}$$ $$n_\text{total}=n_1+n_2=0.15\ \mathrm{mol}+0.06\ \mathrm{mol}=0.21\ \mathrm{mol}$$ New concentration: $$c_\text{new}=\frac{n_\text{total}}{V_\text{total}}=\frac{0.21\ \mathrm{mol}}{0.05\ \mathrm l}= 4.2\ \mathrm{mol\ l^{-1}}$$
