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Question: The actual molecular mass of chlorine is: A. \(58.93 \times {10^ - }^{24}g\) B. \(117.9 \times {...

The actual molecular mass of chlorine is:
A. 58.93×10−24g58.93 \times {10^ - }^{24}g
B. 117.9×10−34g117.9 \times {10^{ - 34}}g
C. 58.93×10−34g58.93 \times {10^{ - 34}}g
D. 117.9×10−24g117.9 \times {10^{ - 24}}g

Explanation

Solution

Molecular mass is the sum of atomic masses of the elements present in a molecule. It is obtained by multiplying the atomic mass of each element by the number of its atoms and adding them together.

Complete step by step answer:
To solve this question, first identify that chlorine is a monoatomic, diatomic or triatomic molecule. Afterwards use atomic mass to find the molecular weight or molar mass of chlorine. The product of atomic number and number atoms is called molecular weight.
So, chlorine exists as a diatomic molecule and the atomic number of chlorine is 17. The atomic mass of chlorine is 35.5g/mole.
To find molecular mass of chlorine, the formula of chlorine is Cl2C{l_2}
Molecular mass of chlorine=(2×35.5)a.m.u = \left( {2 \times 35.5} \right)a.m.u
∴\therefore Molecular mass of chlorine is=71 a.m.u = 71{\text{ }}a.m.u
We know that, 11 atomic mass unit=112×mass  of  one  C−atom = \dfrac{1}{{12}} \times mass\,\,of\,\,one\,\,C - atom …… (i)
To find mass of one C−C - atom
Mass of one C−C - atom=atomic mass of carbonAvogadro′s number = \dfrac{{atomic{\text{ mass of carbon}}}}{{Avogadro's{\text{ number}}}}
Where (atomic mass of carbon=12g = 12g, Avogadro’s number=6.022×1023 = 6.022 \times {10^{23}})
∴\therefore Mass of one C−C - atom=(126.022×1023)g = \left( {\dfrac{{12}}{{6.022 \times {{10}^{23}}}}} \right)g
⇒\Rightarrow Mass of one C−C - atom=(1.99×10−23)g = \left( {1.99 \times {{10}^{ - 23}}} \right)g
Then to find 1 atomic mass unit (a.m.u)
From equation (i), we get
11 atomic mass unit (a.m.u)=112×mass  of  one  C−atom = \dfrac{1}{{12}} \times mass\,\,of\,\,one\,\,C - atom
∴\therefore 1 atomic mass unit (a.m.u)=(112×1.99×10−23)g = \left( {\dfrac{1}{{12}} \times 1.99 \times {{10}^{ - 23}}} \right)g
=(1.66×10−24)g= (1.66 \times {10^{ - 24}})g.
To find the actual molecular mass of chlorine
Molecular mass of chlorine=71×1a.m.u = 71 \times 1a.m.u
=(71×1.66×10−24)g= (71 \times 1.66 \times {10^{ - 24}})g
=(117.86×10−24)g= (117.86 \times {10^{ - 24}})g
Hence, the correct option is D.

Note: Molecular mass of chlorine is mass of one chlorine molecule. The actual mass is different from the gram atomic mass. Molecular mass is a very small value which must be calculated carefully considering the powers in a proper way. It should not be taken as molecular mass because generally molecular mass represents the gram molecular mass.