Final answer:
The concentration of phenol red indicator in an Olympic-sized swimming pool after dissolving 3.5 grams of the indicator would be 1.017 ppb, calculated using the pool's volume and the mass of solution.
Step-by-step explanation:
To calculate the concentration of phenol red indicator in parts per billion (ppb) in an Olympic-sized swimming pool, we first need to determine the volume of the pool. The pool's dimensions are given as 50.0 meters in length, 25.0 meters in width, and an average depth of 2.75 meters. The volume V of the pool can be calculated using the formula V = length \(\times\) width \(\times\) depth.
V = 50.0 m \(\times\) 25.0 m \(\times\) 2.75 m = 3437.5 m^3
To convert the pool volume to kilograms (since 1 cubic meter of water is approximately 1000 kg), we multiply by 1000:
Mass of the solution = 3437.5 m^3 \(\times\) 1000 kg/m^3 = 3437500 kg
Next, to find the concentration in ppb, we use the formula defined as the ratio of solute-to-solution mass multiplied by 10^9:
Concentration (ppb) = (mass of solute/mass of solution) \(\times\) 10^9
Given that the mass of the solute (phenol red indicator) is 3.5 grams, we can now calculate the concentration:
Concentration (ppb) = (3.5 g / 3437500 kg) \(\times\) 10^9
Since 1 gram is equal to 10^6 micrograms (µg), we first convert the solute mass to µg:
3.5 g = 3.5 \(\times\) 10^6 µg
Now, we can calculate the concentration in ppb:
Concentration (ppb) = (3.5 \(\times\) 10^6 µg / 3437500 kg) \(\times\) 10^9
= 1.017 ppb.