Calculating the mass?????

Question

Calculate the mass in grams of solid sodium hypochlorite that would need to be added to a swimming pool of volume 1.5 x 10^4 gallons to achieve a chlorine (not hypchlorite ion) concentration of 3ppm. Note: 1 gallon is 3.79 liters and the density of the pool water is 1.0g/mL.

Thanks sooooo much for the help!! I appreciate it!!!

Answer 1

3 ppm is 3 parts per million. But parts-per notation can be ambiguous; it can mean a ratio of numbers of particles, or it can refer to mass ratios. I'll assume it means mass here, simply because you wouldn't actually have any free particles of chlorine. In the case of an aqueous solution, 1 ppm is equivalent to 1 mg/mL, so 3 pmm is 3 mg/mL.

You need to know the volume of water. Simply convert the volume of the water from gallons to mL by multiplying the number of gallons by (3.79 L / gal)(1000 mL / L).

Sodium Hypochlorite is NaClO. Calculate the molecular mass of this substance, and also note the atomic mass of chlorine. You will now know the volume V of the water in mL. Your required mass of chlorine, in mg, will therefore be 3V. However, the chlorine comes along with the rest of the solid sodium hypochlorite. So multiply 3V by the ratio of the molecular mass of NaClO to the atomic mass of chlorine in order to get the total mass of the sodium hypochlorite you must add. This gives you a mass in mg. Divide by 1000 to get the mass in grams.