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Question: The Statue of Liberty is made of \(2.0\times {{10}^{5}}lbs\) of copper sheets bolted to a framework ...

The Statue of Liberty is made of 2.0×105lbs2.0\times {{10}^{5}}lbs of copper sheets bolted to a framework (1 lb=454 g)(1\text{ }lb=454\text{ }g) . How many atoms of copper are there on the statue? The atomic weight of Cu = 63.5)
(A)- 2.1×10272.1\times {{10}^{27}}
(B)- 8.6×10298.6\times {{10}^{29}}
(C)- 4.3×10264.3\times {{10}^{26}}
(D)- 8.6×10268.6\times {{10}^{26}}

Explanation

Solution

The mole concept is the convenient method of expressing the amount of substance present in any compound or molecule. One mole of any substance is defined as the amount of a substance that contains exactly 6.022×10236.022\times {{10}^{23}} elementary entities of the given substance.

Complete answer:
-The number 6.02214076×10236.02214076\times {{10}^{23}} is known as the Avagadro’s constant which is often represented as NA or N0{{N}_{A}}\text{ or }{{\text{N}}_{0}} .
-The number of moles of any molecule is not always equal to the number of moles of its constituent elements. For example, according to the mole concept, one mole of water contains NA{{N}_{A}} number of water molecules. However, each water molecule is made up of 2 moles of hydrogen and one oxygen atom. Therefore, we can say that one mole of water contains 2 moles of hydrogen and one mole of oxygen.
-The number of moles in a given sample of an element or compound can be calculated using the formula-
Number of moles = Given mass Molar mass\text{Number of moles = }\dfrac{\text{Given mass }}{\text{Molar mass}}
-According to question,
Given the mass of copper =2×105 lbs=2×105×454g=9.08×107g(∵1 lb = 454 g)=2\times {{10}^{5\text{ }}}lbs=2\times {{10}^{5}}\times 454g=9.08\times {{10}^{7}}g(\because 1\text{ lb = 454 g)}
Molecular weight of copper = 63.5 g/moles
Number of moles of copper =2×105×45463.5=\dfrac{2\times {{10}^{5}}\times 454}{63.5}
Number of atoms of copper on the statue =2×105×45463.5×6.023×1023=8.6×1029atoms=\dfrac{2\times {{10}^{5}}\times 454}{63.5}\times 6.023\times {{10}^{23}}=8.6\times {{10}^{29}}atoms

Therefore, the correct answer is option D.

Note:
There are some related terms among which you must not get confused. The total number of moles in a given substance is calculated from the formula given above. For calculating the total number of atoms or molecules in a sample, we will use the following formula-
Number of atoms or molecules = Number of moles×(6.022×1023)\text{Number of atoms or molecules = Number of moles}\times (\text{6}\text{.022}\times \text{1}{{\text{0}}^{23}})
The relationship between the atomic mass unit (amu) and the gram is given by-
1 amu = 1 gram6.022×1023=1.66×10−24 grams1\text{ amu = }\dfrac{1\text{ gram}}{6.022\times {{10}^{23}}}=1.66\times {{10}^{-24}}\text{ grams}