Respuesta :
Answer:
[tex]3.34\times 10^{26}[/tex] electrons
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 = [tex]\rho\ =\ 1000 g/L[/tex]
let m be the mass of the water,
[tex]\therefore m\ =\ \rho\times v\\\Rightarrow m\ =\ 1000\times 1\\\Rightarrow m\ =\ 1000\ g[/tex]
Now, number of moles is equal to the ratio of the mass of the substance and the molecular weight of the substance.
[tex]\therefore n\ =\ \dfrac{m}{M}\\\Rightarrow n\ =\ \dfrac{1000}{18}\\\Rightarrow n\ =\ 55.55\ moles[/tex]
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.
[tex]\therefore[/tex] number of molecules = [tex]55.55\times 6.022\times 10^23\ =\ 334.56\times 10^{23} molecules[/tex]
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 = [tex]10\times 334.56\times 10^{23}\ =\ 3.34\times 10^{26} electrons.[/tex]
Answer:
(a) [tex]3.3456\times 10^{26}\ electrons[/tex]
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:
[tex]\textrm{Number of moles of water} = \dfrac{\textrm{Mass of water}}{\textrm{Mass per unit mole of water}}\\\Rightarrow n = \dfrac{1000\ g}{18.0\ g/mol}\\\Rightarrow n =55.55\ mol[/tex]
Since, 1 mole of any substance contains [tex]6.022\times 10^{23}[/tex] atoms.
Let us calculate the total number of molecules of water which is given by:
[tex]\textrm{Total number of molecules of water}=\textrm{Total moles of water}\times \textrm{Avogadro number}\\\Rightarrow N = n\times N_a\\\Rightarrow N = 55.55\times 6.022\times 10^{23}}\\\Rightarrow N = 3.3456\times 10^{25}\ molecules[/tex]
Since one molecule of water contains 10 electrons. So, the given number of molecules of water contains the following electrons which is as:
[tex]\textrm{Number of electrons}=\textrm{Number of water molecules}\times \textrm{Number of electrons in one water molecule}\\\Rightarrow m = 3.3456\times 10^{26}\ molecules\times 10\ electrons/molecule\\\Rightarrow m = 3.3456\times 10^{26}\ electrons.[/tex]
Hence, 1 liter of water contains [tex]3.3456\times 10^{26}[/tex] electrons.
