Final answer:
Using Henry's Law and assuming the Henry's Law constant does not change significantly with small temperature variations, the millimolar concentration of dissolved oxygen in a lake or stream at 12 °C and under Earth's atmospheric partial pressure for oxygen is approximately 0.273 mM.
Step-by-step explanation:
To calculate the millimolar concentration of dissolved oxygen in a lake or stream at 12 °C under Earth's atmospheric partial pressure of oxygen, we need to utilize Henry's Law, which states that the concentration of a gas in a liquid is directly proportional to the partial pressure of that gas above the liquid. The general formula for Henry's Law is:
C = kP
where C is the concentration of the gas in the liquid, k is Henry's law constant, and P is the partial pressure of the gas.
Henry's law constant for O₂ in water at 25°C is given as 1.3 × 10⁻³ M/atm. However, the temperature in our case is 12°C, which might affect the value of k. It is common practice in many scenarios to assume its value doesn't change significantly with small temperature changes, or to adjust k using a temperature correction if a more accurate calculation is needed and the necessary data is available. We also know that the partial pressure of oxygen in Earth's atmosphere is approximately 0.21 atm, as atmospheric pressure is 1 atm and oxygen makes up about 21% of Earth's atmosphere by mole fraction.
Assuming that k remains constant at 1.3 × 10⁻³ M/atm for 12°C, we can proceed to calculate the solubility of oxygen (C) as follows:
C = (1.3 × 10⁻³ M/atm) × (0.21 atm)
C = 2.73 × 10⁻´ M
To express this in millimolar (mM), we convert moles per liter to millimoles per liter (mM) by multiplying by 1,000:
C = 2.73 × 10⁻´ M × 1,000 mM/M
C = 0.273 mM
The millimolar concentration of dissolved oxygen at 12°C under the partial pressure of 0.21 atm of oxygen is approximately 0.273 mM.