Page 175 - Theory and Problems of BEGINNING CHEMISTRY

164 MOLARITY [CHAP. 11

The final volume is 10.0 L, as stated in the problem.
6.00 mol
Molarity = = 0.600 M
10.0L
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.)
0.60 mol
∼
Molarity = = 0.086 M
7.0L
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)If1.0Lof2.0 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
20 mi 40 mi

Distance = 1.0h + 1.0h = 60 mi
1h 1h
60 mi 30 mi
Average speed = =
2.0h 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
2.0 mol 4.0 mol

1.0L + 1.0L = 6.0 mol
1L 1L
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
4.00 mol 2.00 mol

Final number of moles = 3.00 L + 4.00 L = 20.0 mol
1L 1L
20.0 mol
Molarity = = 2.86 M
7.00 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
20.0 mol
Molarity = = 2.00 M
10.0L
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.

11.3. TITRATION
To determine the concentration of a solute in a solution (e.g., HCl) we treat the unknown solution with a
solution of known concentration and volume (e.g., NaOH) until the mole ratio is exactly what is required by the
balanced chemical equation. Then from the known volumes of both solutions, the unknown concentration of the