Problem: The following five beakers, each containing a solution of sodium chloride (NaCl, also known as table salt), were found on a lab shelf:Arrange the solutions in order of decreasing concentration.Molarity (M) is defined as the number of moles of solute divided by the solution volume expressed in liters:Molarity =moles of solutev of solutionFor example, 1 M HCl contains 1 mol of HCl dissolved in 1 L of solution. When a concentrated solution is diluted, the number of moles of solute stays constant; only the volume of the solution is changed. A dilution indicates an increase in solution volume and, therefore, the concentration of the solution must decrease. If you add more water to the HCl solution considered above, so that now the volume is 2 L , the number of moles remains the same but the volume is doubled. Hence the molarity of the solution is now 1 mol in a 2 L solution, that is, (1/ 2) M or 0.5 M.The number of moles of solute before and after dilution can be calculated by multiplying molarity times volume. We can set up the following equations:moles of solute = molarity × volumemoles of solute = Mi × Vi = Mf × Vfwhere Mi is the initial molarity (of the concentrated solution), Vi is the initial volume, Mf is the final molarity (of the diluted solution), and Vf is the final volume. In the HCl solution example the initial molarity is 1 M, the initial volume is 1 L, the final volume is 2 L, and the molarity is 0.5 M. Thus the number of moles present in these solutions isMiVi = MfVf = 1 M × 1 L = 0.5 M × 2 L = 1 mol

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The following five beakers, each containing a solution of sodium chloride (NaCl, also known as table salt), were found on a lab shelf:

Arrange the solutions in order of decreasing concentration.

Molarity (M) is defined as the number of moles of solute divided by the solution volume expressed in liters:

Molarity =moles of solutev of solution

For example, 1 M HCl contains 1 mol of HCl dissolved in 1 L of solution. When a concentrated solution is diluted, the number of moles of solute stays constant; only the volume of the solution is changed. A dilution indicates an increase in solution volume and, therefore, the concentration of the solution must decrease. If you add more water to the HCl solution considered above, so that now the volume is 2 L , the number of moles remains the same but the volume is doubled. Hence the molarity of the solution is now 1 mol in a 2 L solution, that is, (1/ 2) M or 0.5 M.


The number of moles of solute before and after dilution can be calculated by multiplying molarity times volume. We can set up the following equations:

moles of solute = molarity × volume
moles of solute = Mi × Vi = Mf × Vf

where Mi is the initial molarity (of the concentrated solution), Vis the initial volume, Mf is the final molarity (of the diluted solution), and Vf is the final volume. In the HCl solution example the initial molarity is 1 M, the initial volume is 1 L, the final volume is 2 L, and the molarity is 0.5 M. Thus the number of moles present in these solutions is


MiVi = MfVf = 1 M × 1 L = 0.5 M × 2 L = 1 mol

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