a. Assuming that rivers are the only input and that the oceans are in steady sta

Question

a. Assuming that rivers are the only input and that the oceans are in steady state with respect to element K+ calculate the residence time for K+ using the data in the Table below. The mass of the ocean is ~1.4 x 1021 kg and the river flux is 4.6 x 1016 kg yr-1.

       b. If there is additional input of K+ from ridge crest hydrothermal systems equalto about 20% of the river input, how would that change the residence time? Show your calculations in both cases.

Ihe Concentration and Mean Residence Time of the Major Constituents of Ocean Water Average Concentration in Ocean Water Average Chlorinity(mg/kg) Concentration in of Salinity 35 Constituent Sodium Magnesiun Calcium Potassium Strontium (mg/kg)' in Oceans 0.5561 0.06679 0.02127 0.0206 0.00041 (mmol/kg) 468.0 53.2 10.2 10.2 10,760 1,294 412 399 6.9 3.9 15.0 2.1 1.0×10? 8.5×105 5.9 × 106 4 x10 7.9 0.090 Chloride Sulfate Bicarbonate Bromide Boron Fluoride 7.3X10 7.9x 105 1.0000 0.1400 0.00749 0.003473 0.000240 0.000067 2,712 145 545.0 28.2 8.1 0.6 55.9 2.38 0.84 0.39 0.068 1 x107 5 x10 Data from Pytkowicz and Kester (1971). . (mg/kg),e (chlorinity ratio), × 19,350. Sce text for residence time computations. See text for reaidence time computations "Mean of two averages Table 3 Data from Gibbe (1972)

Explanation / Answer

a) Residence time is

residence time = mass of water in the ocean / flux of water to the ocean by river

For any element

Residence Time = Total amount ion in seawater / Input rate

We can calculate the inpur rate as = Average concentration of ion in river X river discharge rate

Input rate = 2.1 mg / Kg X 4.6 X 10^16 Kg / year = 9.66 X 10^16 mg / year = 9.66 X 10^10 Kg / year

total amount in sea water = average concentration X total amount of water = 399 X 10^-6 X 1.4 X 10^21 Kg

= 5.58 X 10^17 Kg
Residence time = 5.58 X 10^17 / 9.66 X 10^10 Kg / year = 5.77 X 10^6 years

b) if addition input of K+ = 20% of the river input

So per year the input rate extra will be = 20 X 9.66 X 10^10 / 100 = 1.932 X 10^10 Kg / year

total input = (9.96 + 1.932 ) X 10^10 = 11.89 X 10^10 Kg / year

So residence time = 5.58 X 10^17 / 11.89 X 10^10 Kg / year = 4.69 X 10^6 years

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