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Question: Number of electrons in 1.8mL of \[{{H}_{2}}O\] are: A. \[6.02\times {{10}^{23}}\] B. \[6.02\time...

Number of electrons in 1.8mL of H2O{{H}_{2}}O are:
A. 6.02×10236.02\times {{10}^{23}}
B. 6.02×10246.02\times {{10}^{24}}
C. 6.02×10226.02\times {{10}^{22}}
D. 6.02×10256.02\times {{10}^{25}}

Explanation

Solution

the electrons are the subatomic particles which hold the elementary negative charge and whose magnitude is equal to the magnitude to the charge held by the proton but with an opposite sign. Electrons are distributed o present around the nuclei of the atomic orbitals and it is the place where the probability of finding the electron is highest. It was discovered by J.J. Thomson in 1897.

Complete step by step solution:
the given volume of water is = 1.8mL
The density of water is = d= 1g/mL
Now the formula of density in terms of volume and mass is the following:
Density= massvolume\dfrac{mass}{volume}

Now the density is equal to the division of mass by volume so the mass will be equal to the volume multiplied by density. So the formula of mass in terms of density and volume is the following:
mass=volume×densitymass=volume\times density
So the formula for mass of water will be
mw=Vd{{m}_{w}}=\dfrac{V}{d}
So now substituting the values we get:
mw=1.8×1{{m}_{w}}=1.8\times 1=1.8g
The molecular mass for 1 mole of water = 1(2)+161(2)+16=18g
Number of moles for water molecules= mwmolecular  weight=1.818=0.1mole\dfrac{{{m}_{w}}}{molecular\; weight}=\dfrac{1.8}{18}=0.1mole
The number of molecules present in water in 18g mass of water, which means the molecules in 0.1mole of water = 6.02×10226.02\times {{10}^{22}} molecules.
Now the number of electrons in 1 molecule of water = 1(2)+8=101(2)+8=10 electrons
So the number of electrons present in 6.02×10226.02\times {{10}^{22}} molecules of water will be
= 6.02\times {{10}^{22}}$$$$\times 10=6.02×10236.02\times {{10}^{23}} electrons.
So the total number of electrons which are present in 1.8 ml of water is 6.02×10236.02\times {{10}^{23}} electrons.

Hence the correct answer is option A.

Note: The 6.02×10236.02\times {{10}^{23}} is the Avogadro number which is used widely for the measurement of units such as atoms, molecules which are present in 1 mole of the substance. It is considered as the proportionality factor which tends to relate between the amount of the substance in sample with constituent particles. The Si unit for aAvogadro number is reciprocal of mole.