How many moles of electrons are in 1mL of water?

[HelloCthulhu]

Homework Statement

How many moles of electrons are in 1mL of H₂O

Homework Equations

[/B]
1mL = 1g

moles to grams conversion - moles x molar mass = grams

mass of 1 electron = 9.109382 x 10^-28g

moles to molecules = number of moles x avogadro's number (6.022140857 × 10²³)

The Attempt at a Solution

[/B]
Molar mass of H₂O
H = 1g, O = 16g, H₂O = 18g

Number of electrons in 1 molecule of H₂O
H = 1e−, O = 8e−, H₂O = 10e−

Moles in 1g of H₂O = 1g/18g = 0.0556M

Molecules in 0.0556M of H₂O
0.0556M x (6.022140857 × 10²³) = 3.348310835 x 10²² molecules

Number of electrons in 0.0556M of H₂O
(3.348310835 x 10²²) molecules x 10e− = 3.348310835 x 10²³e−

Moles of electrons in 0.0556M of H₂O
(3.0501042450753967 x 10⁴g) of e− / 6.022140857 × 10²³ = 0.5556M

 

[Borek]

Final answer looks OK (although it contains way too many significant digits).

mass of 1 electron = 9.109382 x 10^-28g

Is it really needed?

moles to molecules = number of moles x avogadro's number (6.022140857 × 10²³)

No need to use that. Instead of doing several conversions (mass → moles of water → number of molecules → number of electrons → moles of electrons) you can directly calculate number of moles of electrons in known number of moles of water. Just like there are ten electrons per molecules of water there are ten moles of electrons per each mole of water, so just multiplying number of moles of water by ten will give the correct answer (in other words: mass → moles of water → moles of electrons).

 

[HelloCthulhu]

Just like there are ten electrons per molecules of water there are ten moles of electrons per each mole of water

That makes so much more sense! I'll definitely use this approach next time.