Question

When 3 L of 0.5 M NaCl is mixed with 9 L of 0.2777 M of NaCl, determine the concentration of the final solution , assuming that the volumes are additive.
(a) 0.33 M
(B) 0.39 M
(C) 0.5777 M
(D) 0.7777 M
(E) None of the above

Answer 1

Hint: When 2 solutions of the same compound are mixed together then the resultant compound differs in its composition if the molarity of the compounds is different in the original solutions. Thus the resultant volume will not just be the addition of the original volumes.

Complete step by step solution:
-To find the concentration of the final solution, we first need to analyse what is given in the question and what do all the terms mean.
-We are given 2 different solutions of NaCl. They have different volumes originally.Also their molarity is given which is also unequal. So first we need to be thorough with the concept of molarity.
-Molarity, also called molar concentration, is a measure of the solute in a solution. It is defined as the ratio of the moles of the solute per liter of the solution. Its unit is mol/L and is denoted by the letter M.
M = n/v where M=molarity
                         n = moles of solute
                         v = litres of solution.
-We need to remember that the moles of a solute do not change if we dilute a solution. Only the solvent is added during dilution and moles depend on the solute and not the solvent.
So, from the above equation, we can conclude that moles=vol X molarity
                n = M X v
-Now looking at the question, we observe that there are 2 different solutions and they are mixed together. So we can find the molarity by finding the moles of the whole combined solution and then divide it by the volume of the total combined solution.
-We can see that the moles of the original solutions are not given in the question. We can find it and then use it to find the molarity of the solution after mixing the 2 solutions.
-We are given the volume of each solution as well as the molarity of each solution. Thus we can find the individual moles of each solution.
For solution 1, we see that volume is 3L and molarity is 0.5. Thus the moles for this solution will be 3 X 0.5 = 1.5
For solution 2, we see that the volume is 9L and molarity is 0.2777. Thus the moles for this solution will be 9 X 0.2777 = 2.4993.
-Thus the total moles of the combined solution will be 1.5 + 2.4993 = 3.9993.
Now we got the value of total moles. To find molarity, we need the value of total volume also. It is clear that 3L of a solution is added to 9L of another solution. So, the total volume of the combined solution will be 3+9=12.
-Now using the above mentioned formula of molarity, we can find the molarity of the combined solution.
M=n/v = 3.9993/12 = 0.333

Therefore, the molarity or the molar concentration of the combined solution is 0.333 mol/L which is option A.

Note: One thing to keep in mind is that the molarity depends on the volume of the solution and not the solvent.
Solution = solute + solvent.
So, in a solution, the volume is added not only by the solvent but also by the solute. There are certain concepts like molality where we need the physical quantities of solvent and not of solution.