Question

Water has a mass per mole of 18.0 g/mol, and each water molecule (H20) has 10 electrons. (a) How many electrons are there in one liter (1.00 x 10 m ) of water?

Answer 1

(a)
`3.3456* 10^(26)\ electrons`

Step-by-step explanation:

Given:

• Volume of water = 1 L
• Mass per mole of water molecule = 18.0 g/mol
• Number of electrons per molecule of water = 10 electron/mole

Assume:

• Density of water = 1 kg/L

Since the density of water is 1 kg/L. This means 1 L of water has a mass of 1 kg.

Mass of 1 L water = 1 kg = 1000 g

It is given that 1 mole of water molecule weighs 18.0 g. From this value, we can find the number of moles of water molecules in 1000 g water as below:

`\textrm{Number of moles of water} = \frac{\textrm{Mass of water}}{\textrm{Mass per unit mole of water}}\\\Rightarrow n = (1000\ g)/(18.0\ g/mol)\\\Rightarrow n =55.55\ mol`

Since, 1 mole of any substance contains
`6.022* 10^(23)` atoms.

Let us calculate the total number of molecules of water which is given by:

`\textrm{Total number of molecules of water}=\textrm{Total moles of water}* \textrm{Avogadro number}\\\Rightarrow N = n* N_a\\\Rightarrow N = 55.55* 6.022* 10^(23)}\\\Rightarrow N = 3.3456* 10^(25)\ molecules`

Since one molecule of water contains 10 electrons. So, the given number of molecules of water contains the following electrons which is as:

`\textrm{Number of electrons}=\textrm{Number of water molecules}* \textrm{Number of electrons in one water molecule}\\\Rightarrow m = 3.3456* 10^(26)\ molecules* 10\ electrons/molecule\\\Rightarrow m = 3.3456* 10^(26)\ electrons.`

Hence, 1 liter of water contains
`3.3456* 10^(26)` electrons.

Answer 2

`3.34* 10^(26)` electrons

Step-by-step explanation:

Given,

• Molecular mass of the water = M = 18.0 g/mol
• Number of electrons in a water molecules = 10
• volume of the water = v = 1L
• Density of the water =
  `\rho\ =\ 1000 g/L`

let m be the mass of the water,

`\therefore m\ =\ \rho* v\\\Rightarrow m\ =\ 1000* 1\\\Rightarrow m\ =\ 1000\ g`

Now, number of moles is equal to the ratio of the mass of the substance and the molecular weight of the substance.

`\therefore n\ =\ (m)/(M)\\\Rightarrow n\ =\ (1000)/(18)\\\Rightarrow n\ =\ 55.55\ moles`

Hence number of molecules of the water in l L is equal to the product of the number of moles and the Avogadro's number.

`\therefore` number of molecules =
`55.55* 6.022* 10^23\ =\ 334.56* 10^(23) molecules`

Therefore number of electrons in 1L water is equal to the product of the number of electrons in one molecules and the number of molecules,

Hence total number of electrons =
`10* 334.56* 10^(23)\ =\ 3.34* 10^(26) electrons.`