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Most abundant element dissolved in seawater in chlorine at a concentration of 19g/kg of sea water. The volume of earth’s ocean is 1.4×1021l. How many g-atoms of chlorine are potentially available from the oceans? Density of seawater is 1g/ml. (NA=6×1023)
A. 7.5×1020
B. 27×1021
C. 27×1024
D. 7.5×1019

Answer
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Hint: We have to first calculate the total mass of the ocean using the volume of earth’s ocean and density of seawater. Then we have to calculate the total weight of the chloride ions and from the calculated total weight of the chloride ions we have to calculate the number of gram atoms of chlorine.

Complete step by step solution:
Given data contains,
Concentration of chlorine in seawater is 19g/kg.
Volume of the earth’s ocean is 1.4×1021l.
Density of seawater is 1g/ml.
Let us now calculate the total weight of the ocean. We have to multiply the volume of earth’s ocean and density of seawater to get the total weight of the ocean.
Total weight of the ocean=Volume of earth ocean×Density of seawater
We can now substitute the values of volume of earth’s ocean and the density of seawater in the formula that is used to calculate the total weight of the ocean.
Total weight of the ocean=1.4×1021L×1×103gL
Total weight of the ocean=1.4×1024g
The total weight of the ocean is 1.4×1024g.
Let us now calculate the concentration of chlorine in water.
[Cl]=19gCl1000gwater
[Cl]=19×103gCl/gwater
The concentration of chlorine in water is 19×103gCl/gwater.
We can calculate the total weight of chloride by taking the product of total weight of ocean and concentration of chlorine in water.
Total weight of chloride=1.4×1024gwater×19×103gClgwater
Total weight of chloride=2.66×1022gCl
So, the total weight of chloride is 2.66×1022gCl.
From the total weight of chloride, we have to calculate the total number of grams of atoms using the mass of chlorine.
We know that the mass of chlorine atoms is 35.45.
So, the number of gram atoms of chlorine is 2.66×102235.45
The number of gram atoms of chlorine=7.5×1020gatoms.
The number of gram atoms of chlorine is 7.5×1020gatoms.
Therefore,option (A) is correct.

Note:
 An alternate approach to solve this problem is,
Given data contains,
Concentration of chlorine in seawater is 19g/kg.
Volume of the earth’s ocean is 1.4×1021l.
Density of seawater is 1g/ml.
Let us now calculate the total weight of the ocean. We have to multiply the volume of earth’s ocean and density of seawater to get the total weight of the ocean.
Total weight of the ocean=Volume of earth ocean×Density of seawater
We can now substitute the values of volume of earth’s ocean and the density of seawater in the formula that is used to calculate the total weight of the ocean.
Total weight of the ocean=1.4×1021L×1×103gL
Total weight of the ocean=1.4×1024g
The total weight of the ocean is 1.4×1021kg.
Let us now calculate the moles of chlorine in seawater.
Molar mass of Cl2 is 71g/mol.
Moles of chlorine=1971
Moles of chlorine=0.267mol
The moles of chlorine is 0.267mol
The moles of Cl2 present in 1.4×1021kg is 1.4×1021×0.267=0.375×1021
The moles of chlorine present in kg of water is 0.375×1021mol.
We can calculate the g-atoms of chlorine by multiplying the moles two times.
Gram-atoms of Cl2=2×0.375×1021
Gram-atoms of Cl2=0.75×1021
Gram-atoms of Cl2=7.5×1020
The gram atoms of Cl2 is 7.5×1020
Therefore,option (A) is correct.
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