Answer to Question #103116 in General Chemistry for aeriel

Question

How will u compare the amount of dissolved oxygen in a mountain lake at 5,000 ft and 18°C with that in a lake near sea level at the same temperature? Explain.

Answer 1

Pressure at the sea level: 1 atm.

Pressure at 5000 ft: 0.836 atm. Why? Write hypsometric equation:

$p_2=p_1\text{ exp}\bigg[\frac{g(Z_1-Z_2)}{R_dT}\bigg]=\\ \space\\ =1\text{ exp}\bigg[\frac{9.81(0-5000\text{ ft}\cdot0.3048\text{ m/ft})}{287.04\cdot(18+273.15)}\bigg]=0.836\text{ atm}.$

Now refer to Tromans (1998) to calculate the molal concentration of oxygen dissolved in water:

$c_\text{aq}=P_{\text{O}_2}\text{exp}\bigg[\frac{0.046T^2+203.35T\text{ ln}(T/298)-(29.378+0.092T)(T-298)-20591}{8.3144T}\bigg],$

where temperature is in kelvins, pressure is in atm:

$c_\text{aq}(0\text{ ft})=1.447\cdot10^{-3}\text{ mol/kg},\\ c_\text{aq}(5000\text{ ft})=1.210\cdot10^{-3}\text{ mol/kg}.$

References:

Tromans, D. (1998). Temperature and pressure dependent solubility of oxygen in water: a thermodynamic analysis. Hydrometallurgy, 48(3), 327-342. doi: 10.1016/s0304-386x(98)00007-3