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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.

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    $\begingroup$ Please note that the proper term for "number of moles" is amount of substance. The former would be the same as referring to the mass as "number of kilograms". (cc @safdar ) $\endgroup$ – Martin - マーチン Aug 8 '20 at 17:10
  • $\begingroup$ Please also note that descriptive terms or names of quantities shall not be arranged in the form of an equation; i.e. do not write "$\text{volume}=\frac{\text{amount of substance}}{\text{concentration}}$"; write $V=\frac nc$ instead. $\endgroup$ – user7951 Aug 8 '20 at 17:43
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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.

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  • $\begingroup$ Ok, thank you, I had tried that. C=no of moles/volume. Following that I get (3/0.020)+(5/0.05) = 250. However the answer is supposedly 4.5M. I'm sorry to appear slow, but I haven't done this before! $\endgroup$ – Anasutashia Dec 6 '15 at 23:32
  • $\begingroup$ I meant 4.2M instead of 4.5M as the answer given. $\endgroup$ – Anasutashia Dec 6 '15 at 23:51
  • $\begingroup$ Ok, found an equation - (20/50) * 3 + (30/50)*5 = 4.2M $\endgroup$ – Anasutashia Dec 6 '15 at 23:54
  • $\begingroup$ Remember 3M stands for 3 mol/L (the concentration), not 3 moles. So again you were actually dividing the concentration by the volume which gives moles/L/L. Your new equation is correct because e.g. for the first solution, you have diluted 20ml to 50ml, so the new concentration will be 2/5 of the original concentration. Alternatively you could calculate the number of moles of each, add them and then divide by the total concentration to gives the concentration in mol/L or M. I hope that helps you understand the formulas $\endgroup$ – k-- Dec 7 '15 at 0:45
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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: $$c_\text{new}=\frac{n_\text{total}}{V_\text{total}}=\frac{0.21\ \mathrm{mol}}{0.05\ \mathrm l}= 4.2\ \mathrm{mol\ l^{-1}}$$

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