Avg PO4^3- []'s in the deep and surface ocn's are 2.11 and 0.71umolkg^-1. Calc the residence time of PO4^3- in the deep ocn considering the carbon budget(Figure below) Write the general equation, calculation and units.
------ represents a Box outline
Surface---------------------------------
[P]surface
------------/\-----------------;;;;-----
---------\/--------------------;;;;-----
(arrows moving up and down through surface and deep) ventilation =4.6 m/y
;;;;=(sinking)
Jc = 5.0Gt/y
deep------------;;;;--------------------
----------------;;;;--------------------
;;;;=(sinking)
Bc = 0.15Gt/y
sediments-------------------------------
To calculate the residence time of PO4^3- in the deep ocean, you will need to use the carbon cycle budget information provided.
First, we need to convert the given average concentrations of PO4^3- in the deep and surface oceans from micromoles per kilogram (umolkg^-1) to gigatons (Gt). This conversion can be done using the molar mass of PO4^3- (94.97 g/mol) and the density of sea water (approximately 1.03 kg/L)
To convert umolkg^-1 to Gt, we use the following equation:
Average concentration in Gt = (Average concentration in umolkg^-1) * (Total mass of the ocean in Gt) / (1e12 umol/Gt)
The total mass of the ocean can be estimated as the product of the ocean's volume and the density of seawater. Assuming that the ocean has a volume of 1.35 billion cubic kilometers (1.35e18 L), the total mass of the ocean can be calculated as follows:
Total mass of the ocean in Gt = (Ocean volume in L) * (Density of seawater in Gt/L)
Now, we can plug in the given average concentrations of PO4^3- in the deep and surface oceans and calculate their respective values in Gt. Let's assume the deep concentration is denoted as [P]deep and the surface concentration as [P]surface.
[P]deep = (2.11 umol/kg) * (Total mass of the ocean in Gt) / (1e12 umol/Gt)
[P]surface = (0.71 umol/kg) * (Total mass of the ocean in Gt) / (1e12 umol/Gt)
Next, we can calculate the residence time of PO4^3- in the deep ocean using the equation:
Residence time (T) = (Concentration in deep ocean - Concentration in sediments) / (Input flux)
The input flux of PO4^3- is given as Jc = 5.0 Gt/year.
Residence time (T) = ([P]deep - [P]sediments) / Jc
Finally, we can substitute the values calculated earlier to find the residence time of PO4^3- in the deep ocean. The value of [P]sediments is not provided, so you would need additional information to calculate it accurately.