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Question: The number of molecules in 18 mg of water in terms of Avogadro’s number ‘N’ is: A. \[{{10}^{-3}}N\...

The number of molecules in 18 mg of water in terms of Avogadro’s number ‘N’ is:
A. 10−3N{{10}^{-3}}N
B. 10−2N{{10}^{-2}}N
C. 10−1N{{10}^{-1}}N
D. 10 N

Explanation

Solution

Hint: To solve these types of questions, we have to first find the number of moles of the given substance present in the given mass. Now, we know the number of molecules in 1 mole of substance is given by the Avogadro number, denoted by ‘N’. The formula for finding the number of moles is given below:
Number of moles=WeightMolarmassNumber\text{ }of\text{ }moles=\dfrac{Weight}{Molarmass} ​. N=6.023×1023N=6.023\times {{10}^{23}}

Complete answer:
Given,
Weight of water =18mg=18×10−3g=18mg=18\times {{10}^{-3}}g
Molar mass of water = 18 g
Formula used:
Number of moles=WeightMolarmassNumber\text{ }of\text{ }moles=\dfrac{Weight}{Molarmass}

Now substituting the values in the above formula we get,
Number of moles =18×10−318=1×10−3molesNumber\text{ }of\text{ }moles~=\dfrac{18\times {{10}^{-3}}}{18}=1\times {{10}^{-3}}moles
Number of molecules = Number of moles × Avogadro’s numberNumber\text{ }of\text{ }molecules~=~Number\text{ }of\text{ }moles~\times ~Avogadro’s\text{ }number
=1×10−3×N=1\times {{10}^{-3}}\times N
=10−3N={{10}^{-3}}N

Hence, option A is correct which is there are 10−3N{{10}^{-3}}N number of molecules in 18 mg of water in terms of Avogadro’s number ‘N’

Note: The mole (symbol: mol) is the unit of measurement for the amount of substance in the International System of Units (SI). A mole of a substance or a mole of particles is defined as exactly N=6.023×1023N=6.023\times {{10}^{23}} number of particles, which may be atoms, molecules, ions, or electrons etc.