Consider a segment of water in the ocean that has a saturation solubility of 7.5 mg/L of O2. If there are algae in this body of water consuming CO2 at 1.0 mg/hr, how quickly will the water reach saturation if it starts at no O2 dissolved?

To determine how quickly the water will reach saturation, we need to calculate the rate at which oxygen is being dissolved in the water and compare it to the consumption rate by the algae.

First, let's convert the saturation solubility from mg/L to mg/hr. Since we are given the solubility per liter, we can assume a rate of 1 liter of water. Therefore, the saturation solubility of O2 is 7.5 mg/L * 1 L = 7.5 mg/hr.

Next, we need to calculate the rate at which oxygen is being dissolved in the water. The rate of oxygen dissolution can be determined using Henry's Law, which states that the concentration of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid. In this case, we assume that the partial pressure of oxygen in the atmosphere is constant.

Now, let's determine the partial pressure of oxygen in the atmosphere. The partial pressure of oxygen in dry air is approximately 21% of atmospheric pressure, which is about 160 mmHg or 21.32 kPa.

Using Henry's Law, we can calculate the rate of oxygen dissolution in the water. Let's assume a Henry's Law constant (K) of 0.0233 mol/L·atm at 25°C. The molar mass of O2 is approximately 32 g/mol.

Partial pressure of oxygen in the atmosphere = 21.32 kPa
Convert partial pressure from kPa to atm: 21.32 kPa / 101.325 kPa = 0.2104 atm

Rate of oxygen dissolution = K * partial pressure of oxygen in the atmosphere
Rate of oxygen dissolution = 0.0233 mol/L·atm * 0.2104 atm = 0.0049 mol/(L·hr)

Finally, let's calculate how quickly the water will reach saturation by comparing the rate of oxygen dissolution with the rate at which the algae consumes CO2.

Rate of reaching saturation = 7.5 mg/hr (saturation solubility) / 0.0049 mmol/hr (rate of oxygen dissolution)

First, convert mg to mmol:
7.5 mg = 7.5 mg * (1 g / 1000 mg) * (1 mol / 32 g) = 0.234 mmol

Rate of reaching saturation = 0.234 mmol / 0.0049 mmol/hr = 47.8 hr

Therefore, the water will reach saturation in approximately 47.8 hours if it starts with no dissolved oxygen and the algae consumes CO2 at a rate of 1.0 mg/hr.