Mixing two solutions to find overall solution

If you mix 20ml of 3m sugar solution with 30ml of a 5M sugar solution, what solution do you end up with?

I did; volume = number of moles/concerntration - 3/.02 = 150 - 5/.03 = 166.6666667 - 150+166.6666667 = 316.6666667 - wrong answer. Any formulas which could help would be appreciated.

• geeze... $$(20*3) + (30*5) = 50*X$$ – MaxW Dec 6 '15 at 23:01

2 Answers

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.

• 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! – Anasutashia Dec 6 '15 at 23:32
• I meant 4.2M instead of 4.5M as the answer given. – Anasutashia Dec 6 '15 at 23:51
• Ok, found an equation - (20/50) * 3 + (30/50)*5 = 4.2M – Anasutashia Dec 6 '15 at 23:54
• 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 – k-- Dec 7 '15 at 0:45

remember two solutions of different concentrations are mixed together, the total number of moles of the solution is the sum of the moles of the individual solutions. when you get the sum of the moles, u add their volumes and use those two to determine the new concentration of the solution number of moles= .02*3=.06moles number of moles=.03*5=.015moles .015+.06=.21moles total new concentration= .21moles/total volume (.05L)= 4.2M

I hope that helps.