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Question: Each mole of tear gas, lewisite contains 2 hydrogen atoms, \[1.78{\text{ }} \times {10^{ - 22}}\]gra...

Each mole of tear gas, lewisite contains 2 hydrogen atoms, 1.78 ×10−221.78{\text{ }} \times {10^{ - 22}}gram chlorine, 2 carbon atoms and 1.25 ×10−221.25{\text{ }} \times {10^{ - 22}}gram of an unknown metal. its molecular weight will be
A. 178
B. 208
C. 245
D. 342

Explanation

Solution

In the given question we have to calculate the molecular weight of the lewisite which is a tear gas, and has hydrogen and chlorine atoms along with some unknown metal. We will calculate the molecular weight by combining all the weight of atoms given in it followed by dividing it by weight of one atomic mass.

Complete Step by step answer: As we know that a one atomic mass unit mass is exactly equal to one-twelfth mass of carbon-12 atom.
So, the one atomic mass unit is,1amu = 1.661×10−241amu{\text{ }} = {\text{ }}1.661 \times {10^{ - 24}} grams
So, the atomic mass unit of two hydrogen atoms will be
2H2Hatoms = 2×1.661×10−24=3.322×10−24 = {\text{ }}2 \times 1.661 \times {10^{ - 24}} = 3.322 \times {10^{ - 24}}grams
the atomic mass unit of two carbon atoms will be
2C2Catoms = 2 ×12 ×1.661 ×10−242{\text{ }} \times 12{\text{ }} \times 1.661{\text{ }} \times {10^{ - 24}}=  39.864×10−24\;39.864 \times {10^{ - 24}} grams
Similarly, weight of chlorine = 178 ×10−24 = {\text{ }}178{\text{ }} \times {10^{ - 24}} grams
Therefore, the unknown metal weight = 125 ×10−24125{\text{ }} \times {10^{ - 24}}grams
By adding all the weight, we will get the weight of the whole molecule
So, weight of molecule = 1.661×10-24 + 3.322×10−243.322 \times {10^{ - 24}}+  39.864×10−24\;39.864 \times {10^{ - 24}}+  178 ×10−24{\text{ }}178{\text{ }} \times {10^{ - 24}}+ 125 ×10−24125{\text{ }} \times {10^{ - 24}}
= 346.180 ×10−24= {\text{ }}346.180{\text{ }} \times {10^{ - 24}}
The mass of single molecule will be
  = 346.180 ×10−241.661×10−24\; = {\text{ }}\dfrac{{346.180{\text{ }} \times {{10}^{ - 24}}}}{{1.661 \times {{10}^{ - 24}}}}
The mass of single molecule will be =208.42amu = 208.42amu

Hence option B is correct.

Note: Tear gas, formally known as a lachrymator agent or lachrymator the Latin word lacrima which means tear in Latin, though it stimulates the nerves of the lacrimal gland in the eye which produce tears frequently. The compound 2-chlorobenzalmalononitrile is mainly the tear gas compound, has chemical formulaC10H5ClN2{C_{10}}{H_5}Cl{N_2}, and is a cyanocarbon.