Question

Water has a mass per mole of 18.0 g/mol, and each water molecule (H2O) has 10 electrons. (a) How many electrons are there in 3.77 liters of water? (1 liter is equivalent to 1.00 × 10-3 m3) (b) What is the net charge of all these electrons?

Answer 1

Given,

Mass per mole = 18 g/mol

Number of e^- in 1 water molecule = 10 e^-

(a) 18 g of water = 1 mole

Converting grams into liters: 1 gram = 10^-3 liters

Therefore,

18 g of water = 18 * 10^-3 liters

=> 18 * 10^-3 liters of water = 1 mole

So,

But we know that, 1 mole = 6.022 * 10²³ molecules (Avogadro number)

=> 20.9 * 10⁵ moles of water = (20.9 * 10⁵ ) * (6.022 * 10²³) molecules

= (20.9 * 6.022 ) * (10⁵ * 10²³) molecules

= (20.9 * 6.022 ) * 10²⁸ molecules

​​​​​​= 125.86 * 10²⁸ molecules

Now, 1 molecule of water contains 10 electrons.

Therefore,

125.86 * 10²⁸ molecules of water contains = (125.86 * 10²⁸ ) * 10 electrons

= (125.86 ) 10²⁸ * 10 electrons

= (125.86 ) 10²⁹ electrons

= 125.86 * 10²⁹ electrons

(b) Charge on 1 electron = 1.602 * 10^-19 Coulombs

So,

Charge on 12.59 * 10²⁹ electrons = (12.59 * 10²⁹) * (1.602 * 10^-19)Coulombs

= (12.59 * 1.602) * (10²⁹ * 10^-19)Coulombs

= (12.59 * 1.602) * 10¹⁰ Coulombs

= (12.59 * 1.602) * 10¹⁰ Coulombs