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Question: In a gravimetric determination of \[{{{P}}_{{1}}}\] an aqueous solution of dihydrogen phosphate ion ...

In a gravimetric determination of P1{{{P}}_{{1}}} an aqueous solution of dihydrogen phosphate ion H2PO4{{{H}}_{{2}}}{{PO}}_{{4}}^{{ - }} is treated with the mixture of ammonium and magnesium ions to precipitate magnesium ammonium phosphate, Mg(NH4)PO4.6H2O{{Mg(N}}{{{H}}_{{4}}}{{)P}}{{{O}}_{{4}}}{{.6}}{{{H}}_{{2}}}{{O}}. This is heated and decomposed to magnesium pyrophosphate, Mg2P2O7{{M}}{{{g}}_{{2}}}{{{P}}_{{2}}}{{{O}}_{{7}}} which is weighted. A solution of H2PO4{{{H}}_{{2}}}{{PO}}_{{4}}^{{ - }} yielded 1.054 g of Mg2P2O7{{M}}{{{g}}_{{2}}}{{{P}}_{{2}}}{{{O}}_{{7}}}. What weight of NaH2PO4{{Na}}{{{H}}_{{2}}}{{P}}{{{O}}_{{4}}} what present originally?
A.1.14 g
B.1.62 g
C.2.34 g
D.1.33 g

Explanation

Solution

The method used to determine the concentration or mass of a substance by measuring the change in mass is Gravitational analysis. The amount of an analyte can be determined from the mass of the compound and the change in the concentration or mass. NaH2PO4{{Na}}{{{H}}_{{2}}}{{P}}{{{O}}_{{4}}} is also known as monosodium phosphate which is used to detect magnesium ions from salts, used as a food additive.

Complete step by step answer:
The given reactions are:
H2PO4Mg(NH4)PO4.6H2OheatMg2P2O7{{{H}}_{{2}}}{{PO}}_{{4}}^{{ - }} \to {{Mg(N}}{{{H}}_{{4}}}{{)P}}{{{O}}_{{4}}}{{.6}}{{{H}}_{{2}}}{{O}}\xrightarrow[{{{heat}}}]{}{{M}}{{{g}}_{{2}}}{{{P}}_{{2}}}{{{O}}_{{7}}}
Mg2P2O7NaH2PO4{{M}}{{{g}}_{{2}}}{{{P}}_{{2}}}{{{O}}_{{7}}} \to {{Na}}{{{H}}_{{2}}}{{P}}{{{O}}_{{4}}}
The first reaction shows the formation of magnesium pyrophosphate on heating, whereas in the second reaction sodium dihydrogen phosphate is obtained from magnesium pyrophosphate.
Here the weight of Mg2P2O7{{M}}{{{g}}_{{2}}}{{{P}}_{{2}}}{{{O}}_{{7}}} (Magnesium pyrophosphate) ==1.054 g
Applying, POAC (Principle of Atom Conservation) on Mg2P2O7{{M}}{{{g}}_{{2}}}{{{P}}_{{2}}}{{{O}}_{{7}}} and NaH2PO4{{Na}}{{{H}}_{{2}}}{{P}}{{{O}}_{{4}}} on P atom (since P atom is conserved).
1 mole of NaH2PO4{{Na}}{{{H}}_{{2}}}{{P}}{{{O}}_{{4}}} contains 1 mole of P and 1 mole of Mg2P2O7{{M}}{{{g}}_{{2}}}{{{P}}_{{2}}}{{{O}}_{{7}}} contains 2 moles of P.
1×(wt.ofNaH2PO4)(mol.wtofNaH2PO4)=2×(wt.ofMg2P2O7)(mol.wtofMg2P2O7)\Rightarrow {{1}}\,{{ \times }}\,\dfrac{{\left( {{{wt}}{{.}}\,{{of}}\,\,{{Na}}{{{H}}_{{2}}}{{P}}{{{O}}_{{4}}}} \right)}}{{\left( {{{mol}}{{.}}\,{{wt}}\,{{of}}\,{{Na}}{{{H}}_{{2}}}{{P}}{{{O}}_{{4}}}} \right)}}\,{{ = }}\,{{2}}\,{{ \times }}\,\dfrac{{\left( {{{wt}}{{.}}\,{{of}}\,\,{{M}}{{{g}}_{{2}}}{{{P}}_{{2}}}{{{O}}_{{7}}}} \right)}}{{\left( {{{mol}}{{.}}\,{{wt}}\,{{of}}\,{{M}}{{{g}}_{{2}}}{{{P}}_{{2}}}{{{O}}_{{7}}}\,} \right)}}
(wt.ofNaH2PO4)120=2×1.054222\Rightarrow \dfrac{{\left( {{{wt}}{{.}}\,{{of}}\,\,{{Na}}{{{H}}_{{2}}}{{P}}{{{O}}_{{4}}}} \right)}}{{{{120}}}}{{ = 2 \times }}\dfrac{{{{1}}{{.054}}}}{{{{222}}}}
Here, 120 represents the molecular weight of sodium dihydrogen phosphate and 222 represents the molecular weight of magnesium pyrophosphate.
(Now we will put the values given like the weight of Mg2P2O7{{M}}{{{g}}_{{2}}}{{{P}}_{{2}}}{{{O}}_{{7}}} is 1.054 and also we will calculate the molecular masses of NaH2PO4{{Na}}{{{H}}_{{2}}}{{P}}{{{O}}_{{4}}} and Mg2P2O7{{M}}{{{g}}_{{2}}}{{{P}}_{{2}}}{{{O}}_{{7}}}) .
wt.ofNaH2PO4=2×1.054×120222\Rightarrow {{wt}}{{.}}\,{{of}}\,\,{{Na}}{{{H}}_{{2}}}{{P}}{{{O}}_{{4}}}{{ = }}\dfrac{{{{2 \times 1}}{{.054 \times 120}}}}{{{{222}}}}
Weight of NaH2PO4{{Na}}{{{H}}_{{2}}}{{P}}{{{O}}_{{4}}} is 1.139 approx1.141.139 \ approx 1.14
(After calculation we get the value for the weight of NaH2PO4{{Na}}{{{H}}_{{2}}}{{P}}{{{O}}_{{4}}} is 1.139 g which is approximately 1.14 g)
Hence, the correct option is (A).

Note:
The POAC (Principle of Atom Conservation) states that the total number of atoms of the reactants should be equal to the total number of atoms of the products.
The POAC comes from the Law of Conservation of Mass.
Mass of atoms of an element in reactant = Mass of atoms of an element in the product.
The number of atoms of element of the reactants = Number of atoms of element of the product.
Moles of atoms of element of the reactants = Moles of atoms of element of the product.