Exercise 1
Exercise 1 is in two parts: a) and b).
- Use Equation (4) in Section 2.3 to calculate the concentrations of dissolved [latex]He,\ Ne,\ N_{2},\ Ar,\ Kr,[/latex] and [latex]Xe[/latex] (in units of ccSTP/g) in equilibrium with the moist atmosphere at a temperature of 10 °C and an elevation of 450 m above mean sea level. The equation is shown here.
| [latex]C_{i,eq} = \frac{\left( P - e(T) \right)x_{i}}{K_{w,i}(T,S)}[/latex] |
|---|
where:
| [latex]C_{i,eq}[/latex] | = | concentration of air‑saturated water (ASW, ccSTP/g) |
|---|---|---|
| P | = | atmospheric pressure (atm) |
| e(T) | = | vapor pressure of water at temperature T (atm) |
| [latex]K_{w,i}(T,S)[/latex] | = | Henry Coefficient of gas i at temperature T and salinity S (g‑atm/ccSTP) |
| [latex]x_{i}[/latex] | = | fraction of gas i (mixing ratio) in the dry atmosphere |
As with all equations, it is important to use consistent units throughout the calculation (i.e., for Ci,eq in units of ccSTP/g, and P and e in atm, Kw,i should be in g‑atm/ccSTP).
Assume that the recharge salinity is zero. Use Table 1 (Section 2.1) for Henry Coefficient. A good approximation for atmospheric pressure is [latex]P = P_{0}\exp\left( - \frac{Z}{Z_{s}} \right)[/latex] where P0 is the pressure at elevation (Z) of zero (i.e., 1 atm) and [latex]Z_{s}[/latex] is a scaling factor equal to 8,300 as shown in Equation (5). Use the Antoine equation [latex]e = 10^{A - \frac{B}{C + T}}[/latex] where A = ]8.07131, B = 1730.63, C = 233.426 and T is temperature in °C and e is the vapor pressure of water in units of mmHg as shown in Equation (6). Both Equation (5) and Equation (6) follow Equation (4) in Section 2.3. e needs to be converted to units of atm for use in Equation (4).
- Now add 0.003 ccSTP/g of UA to each of these values. On a percentage basis, calculate how much this changes the concentrations relative to the equilibrium values computed in Exercise 1a).