MOLARITY CALCULATIONS

11.2. MOLARITY CALCULATIONS

Molarity, being a ratio, can be used as a factor. Anywhere M (for molar) is used, it can be replaced by mol/L. The reciprocal of molarity can also be used.

EXAMPLE 11.2. How many moles of solute are contained in 3.0 L of 2.0 M solution? Ans.

As usual, the quantity given is put down first and multiplied by a ratio—in this case, the molarity. It is easy to visualize the solution, pictured in Fig. 11-1.

3.0 L

6.0 mol

1L

Fig. 11-1. 3.0 L of 2.0 M solution

EXAMPLE 11.3. What volume of 1.50 M solution contains 6.00 mol of solute?

EXAMPLE 11.4. What is the molarity of a solution prepared by dissolving 63.0 g NaF in enough water to make 250.0 mL of solution?

Ans.

Molarity is defined in moles per liter. We convert each of the quantities given to those used in the definition:

1L

63.0 g NaF

1.50 mol NaF

250.0 mL

= 0.2500 L

42.0 g NaF

EXAMPLE 11.5. What is the concentration of a solution containing 1.23 mmol in 1.00 mL?

1.00 mL 1000 mL

The numeric value is the same in mmol/mL as in mol/L. Thus, molarity can be defined as the number of millimoles of solute per milliliter of solution , which is an advantage because chemists more often use volumes measured in milliliters.

EXAMPLE 11.6. Do we know how much water was added to the solute in Example 11.1? Ans.

We have no way of knowing how much water was added. We know the final volume of the solution, but not the volume of the solvent.

When water is added to a solution, the volume increases but the numbers of moles of the solutes do not change. The molarity of every solute in the solution therefore decreases.

EXAMPLE 11.7. What is the final concentration of 2.00 L of 3.00 M solution if enough water is added to dilute the solution to 10.0 L?

Ans. The concentration is the number of moles of solute per liter of solution, equal to the number of moles of solute divided by the total volume in liters. The original number of moles of solute does not change:

Number of moles = 2.00 L

6.00 mol

1L

The final volume is 10.0 L, as stated in the problem.

6.00 mol

Molarity =

10.0 L = 0.600 M

EXAMPLE 11.8. What is the final concentration of 2.0 L of 0.30 M solution if 5.0 L of water is added to dilute the solution?

Ans. Note the difference between the wording of this example and the prior one. Here the final volume is 7.0 L. (When you mix solutions, unless they have identical compositions, the final volume might not be exactly equal to the sum of the individual volumes. When only dilute aqueous solutions and water are involved, the volumes are very nearly additive, however.)

EXAMPLE 11.9. (a) A car was driven 20 mi/h for 1.0 h and then 40 mi/h for 1.0 h. What was the average speed over the whole trip? (b) If 1.0 L of 2.0 M NaCl solution is added to 1.0 L of 4.0 M NaCl solution, what is the final molarity?

Ans. (a) The average speed is equal to the total distance divided by the total time. The total time is 2.0 h. The total distance is

Distance = 1.0 h

Average speed =

2.0 h = 1h

Note that we cannot merely add the speeds here to get the speed for the entire trip. (b) The final concentration is the total number of moles of NaCl divided by the total volume. The total volume is

about 2.0 L. The total number of moles is

The final concentration is (6.0 mol)/(2.0 L) = 3.0 M. Note that we cannot merely add the concentrations to get the final concentration. (If equal volumes are combined, the concentration is the average of those of the initial solutions.)

EXAMPLE 11.10. Calculate the final concentration if 3.00 L of 4.00 M NaCl and 4.00 L of 2.00 M NaCl are mixed. Ans.

Final volume = 7.00 L Final number of moles = 3.00 L

Note that the answer is reasonable; the final concentration is between the concentrations of the two original solutions. EXAMPLE 11.11. Calculate the final concentration if 3.00 L of 4.00 M NaCl, 4.00 L of 2.00 M NaCl, and 3.00 L of water

are mixed. Ans.

The final volume is about 10.0 L. The final number of moles of NaCl is 20.0 mol, the same as in Example 11.10, since there was no NaCl in the water. Hence, the final concentration is

Note the the concentration is lower than it was in Example 11.10 despite the presence of the same number of moles of NaCl, since there is a greater volume.