Question

What is the mass of water that on electrolysis gives 16.8 L of gas at NTP?

Answer 1

On electrolysis of water the net reaction occurred is represented by the following balanced equation

`2H_2O(l)->2H_2(g)+O_2(g)`

`H_2 and O_2` are are produced in 2:1 mol ratio.So the volumetric ratio under same conditions of temperature and prssure will also be 2:1.

Here total volume of electrolytic gas is 16.8L at NTP. So the volume of `H_2` gas produced is `2/3xx16.8L=11.2L` at NTP.

The above equation suggests that 2mol or `2xx22.4L" "H_2` gas is produced from 2moles or 36g water.

So 11.2L `H_2` at NTP will be produced from `(36g)/(2xx22.4L)xx11.2L`

`=9g" "H_2O`

Answer 2

The mass of the electrolyzed water is 8.39 g.

Explanation:

The balanced equation is

`"2H"_2"O(l)" → "2H"_2"(g)" + "O"_2"(g)"`

We can use the Ideal Gas Law to calculate the number of moles of gas at NTP (20 °C and 1 atm).

`PV = nRT`

`T = "(20 + 273.15) K" = "293.15 K"`

`n = (PV)/(RT) = (1 color(red)(cancel(color(black)("atm"))) × 16.8 color(red)(cancel(color(black)("L"))))/("0.082 06" color(red)(cancel(color(black)("L·atm·K"^"-1")))"mol"^"-1" × 293.15 color(red)(cancel(color(black)("K")))) = "0.6984 mol"`

According to the balanced equation, ⅓ of the moles are oxygen and ⅔ of the moles are hydrogen.

∴ `"Moles of O"_2 = 1/3 × "0.6984 mol" = "0.2328 mol"`

`"Mass of water" = 0.2328 color(red)(cancel(color(black)("mol O"_2))) × (2 color(red)(cancel(color(black)("mol H"_2"O"))))/(1 color(red)(cancel(color(black)("mol O"_2)))) × ("18.02 g H"_2"O")/(1 color(red)(cancel(color(black)("mol O"_2)))) = "8.39 g H"_2"O"`