Answer : The mass of potassium hypochlorite is, 4.1 grams.
Explanation : Given,
pH = 10.20
Volume of water = ![4.50\times 10^2ml=0.45L](https://tex.z-dn.net/?f=4.50%5Ctimes%2010%5E2ml%3D0.45L)
The decomposition of KClO will be :
![KClO\rightarrow K^++ClO^-](https://tex.z-dn.net/?f=KClO%5Crightarrow%20K%5E%2B%2BClO%5E-)
Now the further reaction with water
to give,
![ClO^-+H_2O\rightarrow HClO+OH^-](https://tex.z-dn.net/?f=ClO%5E-%2BH_2O%5Crightarrow%20HClO%2BOH%5E-)
First we have to calculate the pOH.
![pH+pOH=14\\\\pOH=14-pH\\\\pOH=14-10.20=3.8](https://tex.z-dn.net/?f=pH%2BpOH%3D14%5C%5C%5C%5CpOH%3D14-pH%5C%5C%5C%5CpOH%3D14-10.20%3D3.8)
Now we have to calculate the
concentration.
![pOH=-\log [OH^-]](https://tex.z-dn.net/?f=pOH%3D-%5Clog%20%5BOH%5E-%5D)
![3.8=-\log [OH^-]](https://tex.z-dn.net/?f=3.8%3D-%5Clog%20%5BOH%5E-%5D)
![[OH^-]=1.58\times 10^{-4}M](https://tex.z-dn.net/?f=%5BOH%5E-%5D%3D1.58%5Ctimes%2010%5E%7B-4%7DM)
Now we have to calculate the base dissociation constant.
Formula used : ![K_b=\frac{K_w}{K_a}](https://tex.z-dn.net/?f=K_b%3D%5Cfrac%7BK_w%7D%7BK_a%7D)
Now put all the given values in this formula, we get :
![K_b=\frac{1.0\times 10^{-14}}{4.0\times 10^{-8}}=2.5\times 10^{-7}](https://tex.z-dn.net/?f=K_b%3D%5Cfrac%7B1.0%5Ctimes%2010%5E%7B-14%7D%7D%7B4.0%5Ctimes%2010%5E%7B-8%7D%7D%3D2.5%5Ctimes%2010%5E%7B-7%7D)
Now we have to calculate the concentration of
.
The equilibrium constant expression of the reaction is:
![K_b=\frac{[OH^-][HClO]}{[ClO^-]}](https://tex.z-dn.net/?f=K_b%3D%5Cfrac%7B%5BOH%5E-%5D%5BHClO%5D%7D%7B%5BClO%5E-%5D%7D)
As we know that, ![[OH^-]=[HClO]=1.58\times 10^{-4}M](https://tex.z-dn.net/?f=%5BOH%5E-%5D%3D%5BHClO%5D%3D1.58%5Ctimes%2010%5E%7B-4%7DM)
![2.5\times 10^{-7}=\frac{(1.58\times 10^{-4})^2}{[ClO^-]}](https://tex.z-dn.net/?f=2.5%5Ctimes%2010%5E%7B-7%7D%3D%5Cfrac%7B%281.58%5Ctimes%2010%5E%7B-4%7D%29%5E2%7D%7B%5BClO%5E-%5D%7D)
![[ClO^-]=0.0999M](https://tex.z-dn.net/?f=%5BClO%5E-%5D%3D0.0999M)
Now we have to calculate the moles of
.
![\text{Moles of }ClO^-=\text{Molarity of }ClO^-\times \text{Volume of solution}](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20%7DClO%5E-%3D%5Ctext%7BMolarity%20of%20%7DClO%5E-%5Ctimes%20%5Ctext%7BVolume%20of%20solution%7D)
![\text{Moles of }ClO^-=0.0999mole/L\times 0.45L=0.0449mole](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20%7DClO%5E-%3D0.0999mole%2FL%5Ctimes%200.45L%3D0.0449mole)
As we know that, the number of moles of
are equal to the number of moles of KClO.
So, the number of moles of KClO = 0.0449 mole
Now we have to calculate the mass of KClO.
![\text{Mass of }KClO=\text{Moles of }KClO\times \text{Molar mass of }KClO](https://tex.z-dn.net/?f=%5Ctext%7BMass%20of%20%7DKClO%3D%5Ctext%7BMoles%20of%20%7DKClO%5Ctimes%20%5Ctext%7BMolar%20mass%20of%20%7DKClO)
![\text{Mass of }KClO=0.0449mole\times 90.6g/mole=4.07g\approx 4.1g](https://tex.z-dn.net/?f=%5Ctext%7BMass%20of%20%7DKClO%3D0.0449mole%5Ctimes%2090.6g%2Fmole%3D4.07g%5Capprox%204.1g)
Therefore, the mass of potassium hypochlorite is, 4.1 grams.