Question

The charge on 500 cc of water due to proton will be
A) $ 6.1 \times {10^{27}}C $ $ $
B) $ 2.67 \times {10^7}C $
C) $ 6 \times {10^{23}}C $
D) $ 1.67 \times {10^{23}}C $

Answer 1

Hint: According to this question, we need to find out the charge on 500 cc of water due to protons. This question is fully based on the mole concept. Before attempting this question, students must ensure that they have a good understanding of the mole concept. We know that $ 500cc \approx 500ml \approx 500gm $ as the density of water is $ 100kg/{m^3} $ . After knowing this we will apply the formula No. of moles of water = Mass/Molar mass.

Complete step by step answer:
A proton is a subatomic particle with a positive electric charge of +1e elementary charge and a mass slightly less than that of a neutron. Protons and neutrons, each with masses of approximately one atomic mass unit, are jointly referred to as nucleons. The mole is the base unit of amount of substance in the International System of Units. It is defined as exactly 6.02214076×10²³ particles, which may be atoms, molecules, ions, or electrons. The word “mole” was introduced around the year 1896 by the German chemist Wilhelm Ostwald, who derived the term from the Latin word moles meaning a ‘heap’ or ‘pile'.
In $ 500c{m^3} $ of water, density of water is $ 100kg/{m^3} $
Mass of the water $ = $ density × volume
$\Rightarrow $ Mass $ = $ $ 1000 \times \dfrac{{500}}{{1000000}}kg $
$\Rightarrow $ Mass $ = $ $ \dfrac{5}{{10}}kg $
$\Rightarrow $ Mass $ = $ $ 0.5kg $
No. of moles of water $ = $ mass/molar mass
$\Rightarrow $ No. of moles $ = $ $ \dfrac{{0.5}}{{18}} $
$\Rightarrow $ No. of moles $ = $ $ 0.0278 $
Now, one molecule of water contains, $ 2 $ (from hydrogen) + $ 8 $ (from oxygen.) $ = $ $ 10 $ electrons
Now, No. of electrons in one atom $ = $ No. of protons in $ 1 $ atom $ = $ $ 10 $
Now, no. of atoms $ = $ no. of moles $ \times $ Avogadro's number.
No. of electrons $ = $ no. of moles $ \times $ Avogadro's number $ \times $ $ 10 $
$\Rightarrow $ No. of protons $ = $ $ 0.0278 \times 6.022 \times {10^{23}} \times 10 $
So the no. of protons $ = $ $ 1.67 \times {10^{23}} $
Charge due to these protons $ = $ $ 1.67 \times {10^{23}} \times 1.6 \times {10^{ - 19}} $
 $ = $ $ 2.67 \times {10^4} $
Hence, the charge due to protons in 500 cc of water is $ 2.67 \times {10^4} $.

Note:
Be careful while applying the formula. Remember that a proton is a subatomic particle with a positive electric charge of +1e elementary charge and a mass slightly less than that of a neutron.. Calculation mistakes are possible, so try to avoid them and be sure of the final answer. Students must also remember the charge on a proton in order to solve such questions.