Question 3.EP.10: Aqueous solutions of sodium hypochlorite (NaClO) can be used...
Aqueous solutions of sodium hypochlorite (NaClO) can be used in the synthesis of hydrazine (N_{2}H_{4}). Hydrazine has often been used as a rocket fuel, and a derivative of hydrazine is used as a fuel for engines in the orbital maneuvering system of the space shuttle. A solution is prepared by dissolving 45.0 g of NaClO in enough water to produce exactly 750 mL of solution. What is the molarity of the solution?
Strategy
To obtain molarity we need two quantities—moles of solute and liters of solution. Neither of these quantities is given directly in the question, but both can be obtained readily from information given. We must use the molar mass of NaClO to convert from mass to moles and convert the volume from milliliters to liters. Then we can use the definition of molarity to obtain the molarity of the solution.
First we compute the moles of solute.
45.0 \ g \ NaClO \ \times \frac{1.00 \ mol \ NaClO}{74.442 \ g \ NaClO} = 0.604 \ mol \ NaClO
Then convert the solution volume from mL to L:
750 \ mL \ \times \frac{1.00 \ L}{1000 \ mL} = 0.750 \ L
Finally, calculate the molarity:
Molarity =\frac{moles \ of \ solute}{liters \ of \ solution} = \frac{0.604 \ mol}{0.750 \ L}= 0.806 \ M \ NaClO
Analyze Your Answer
Our answer is somewhat smaller than, but fairly close to 1 M. Does this make sense? The amount of NaClO was about 2/3 of a mole and the volume of the solution was 3/4 of a liter. The ratio of 2/3 to 3/4 is 8/9, close to but a little bit smaller than 1, so our result seems reasonable.
Discussion
As usual, this problem could also be set up as a single calculation including the same conversions. Whichever approach you choose, you should always check to be sure that your units work out correctly. Here we have units of mol/L for our answer, which is appropriate for molarity. Confirming this helps avoid careless errors.