Question

On strong heating, 3.64 g of a silver salt of an organic dibasic acid yield 2.1g of silver. If the weight percentage of carbon in it is 8 times the weight percentage of hydrogen and one half the weight percentage of oxygen , then the molecular formula of the acid is:
[Atomic weight of Ag=108]
$
A.{C_4}{H_6}{O_4} \\
B.{C_4}{H_6}{O_6} \\
C.{C_2}{H_6}{O_2} \\
D.{C_5}{H_{10}}{O_5} \\
$

Answer 1

Hint:
Step by step answer: From Avogadro’s law it is known that equal volumes of all gases contain equal numbers of molecules under similar conditions. Now since one mole of molecules of all gases contain the same number (6.022$ \times {10^{23}}$ ) of molecules, therefore they occupy the same volume under similar pressure and temperature. The mass of one mole of atoms is exactly equal to the atomic mass in grams of that element. We are given that 3.64 g of silver salt yields 2.1 g of silver, when we know that 108g which is the molar mass of silver is also one mole of silver. Therefore
108 g of silver=1 mole
2.1g of silver=$\dfrac{1}{{108}} \times 2.1$ =0.02 mole
0.01 mole and 3.64g of silver yelds 0.02 mole, hence the molecular weight of silver salt is 3.64/0.01=364g
Hence 3.64g of silver salt yields 0.01 mole of silver. The silver salt is a dibasic acid which means it has two replaceable acidic hydrogens. Since we are given with the ratio of weight percentage of hydrogen, oxygen and carbon. Therefore if we compare the ratio for 100 g of dibasic acid we will get the molecular formula. Then, substituting the values from the question we get
Let the weight percentage of hydrogen be x, then the weight percentage of carbon will be 8x and oxygen will be 16x.
100=8x+x+16x (since the salt is the composition of oxygen, hydrogen and carbon)
$\Rightarrow$ 100=25x
$\Rightarrow$ x=4g
Hence the weight percentage of hydrogen, carbon and oxygen is 4g, 32g and 64g respectively in 100g of salt. The molecular weight of the dibasic acid is=364-2(108)=364-216=148g. so correspondingly 148g of dibasic acid will have weight percentage as
$
  hydrogen = \dfrac{4}{{100}} \times 148 = 5.92g \\
  Oxygen = \dfrac{{64}}{{100}} \times 148 = 94.72g \\
  carbon = \dfrac{{32}}{{100}} \times 148 = 47.36g \\
$
Therefore the atoms of hydrogen, oxygen and carbon in the molecular formula of dibasic acid will be 6, 6 and 4 respectively.

Therefore the molecular formula of the dibasic acid is ${C_4}{H_6}{O_6}$ and the correct option is B.

Note: A compound is a composition of its molecules, its atoms are arranged in a certain composition. Every atom has its share of weight percentage in the compound. Molecular mass of a compound is the sum of atomic mass of the atoms present in it.