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Question: The weight of \(100\) molecules of each of the following substances is: (a) chlorine gas (b) cal...

The weight of 100100 molecules of each of the following substances is:
(a) chlorine gas
(b) calcium oxide
A. (a) 6.022×10−23g6.022 \times {10^{ - 23}}{\text{g}} (b) 9.29×10−21g9.29 \times {10^{ - 21}}{\text{g}}
B. (a) 11.78×10−23g11.78 \times {10^{ - 23}}{\text{g}} (b) 9.29×10−23g9.29 \times {10^{ - 23}}{\text{g}}
C. (a) 23.96×10−21g23.96 \times {10^{ - 21}}{\text{g}} (b) 9.29×10−23g9.29 \times {10^{ - 23}}{\text{g}}
D. (a) 11.78×10−21g11.78 \times {10^{ - 21}}{\text{g}} (b) 9.29×10−21g9.29 \times {10^{ - 21}}{\text{g}}

Explanation

Solution

Stoichiometry is the study of the quantitative aspects of chemical reactions. Chemical equations are concise representations of chemical reactions. Mole is defined as the quantity of a substance that contains the same number of ultimate particles as are present in 12g12{\text{g}} of carbon−12 - 12.

Complete step by step answer:
Concentration is the amount of solute dissolved in a given amount of solution. There are different types of concentration units. Formula and molecular mass deal with individual atoms and molecules. Mole is the unit that relates the number of particles and mass.
One mole of an element contains 6.022×10236.022 \times {10^{23}} particles. This absolute number is called Avogadro’s number. Mass of one mole of substance is called molar mass. Or molar mass of an element is equal to the molecular weight.
Now let’s consider each substance.
(a) 6.022×10236.022 \times {10^{23}} molecules are contained in 1mol{\text{1mol}} of chlorine which has molar mass of 71g.mol−171{\text{g}}.{\text{mo}}{{\text{l}}^{ - 1}}.
So 100100 molecules are contained in 716.022×1023×100=11.78×10−21g\dfrac{{71}}{{6.022 \times {{10}^{23}}}} \times 100 = 11.78 \times {10^{ - 21}}{\text{g}} chlorine gas.
(b) 6.022×10236.022 \times {10^{23}} molecules are contained in 1mol{\text{1mol}} of calcium oxide which has molar mass of 56g.mol−156{\text{g}}.{\text{mo}}{{\text{l}}^{ - 1}}.
So 100100 molecules are contained in 566.022×1023×100=9.29×10−21g\dfrac{{56}}{{6.022 \times {{10}^{23}}}} \times 100 = 9.29 \times {10^{ - 21}}{\text{g}} chlorine gas.
So the weight of 100100 molecules of chlorine gas is 11.78×10−21g11.78 \times {10^{ - 21}}{\text{g}} and that of calcium oxide is 9.29×10−21g9.29 \times {10^{ - 21}}{\text{g}}.

Hence the correct option is D.

Note:
Moles relate the mass of a single atom in amu{\text{amu}} to the mass in grams. Moles to atoms or molecules conversions can be done by multiplying with Avogadro number. Atoms or molecules to moles conversions can be done by dividing by Avogadro number. Moles to grams conversion is moles times molar mass. Molar mass is the collective name for atomic mass and molecular mass. We use moles to calculate the number of particles, molecules, concentrations, etc. It represents a very large quantity of items.