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 What is the volume strength of 100 ml of  $ {{H}_{2}}{{O}_{2}} $  solution which produces 5.6 liters of oxygen gas at 1 bar and  $ {{0}^{\circ }}C $?

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Last updated date: 25th Jun 2024
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Answer
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Hint: The volume of oxygen produced at STP is equal to the volume strength of hydrogen peroxide multiplied to the volume of the hydrogen peroxide used.


Complete answer:

Volume strength or the percentage strength of hydrogen peroxide is the term which is used to express the concentration of hydrogen peroxide in the form of volume of oxygen which can decompose to form water and oxygen gas.

The equation of decomposition of hydrogen peroxide from water and oxygen gas.

 $ {{H}_{2}}{{O}_{2}}\to {{H}_{2}}O+\dfrac{1}{2}{{O}_{2}} $ 

So,

The volume of oxygen produced at STP is equal to the volume strength of hydrogen peroxide multiplied to the volume of the hydrogen peroxide used.

Volume of oxygen produced = volume strength x volume of  $ {{H}_{2}}{{O}_{2}} $ 

In the question, the volume of oxygen produced = 5.6 liters

This volume has to be converted into ml because the volume of hydrogen peroxide used is given in ml.

So, volume of oxygen = 5.6 x 1000 = 5600 ml

The volume of hydrogen peroxide used = 100 ml.

So,  $ 5600\text{ = volume strength x 100} $ 

 $ \text{volume strength = }\dfrac{5600}{100}=56 $ 

Hence, the volume strength of  $ {{H}_{2}}{{O}_{2}} $  is 56.


Additional Information:

We can relate the volume strength of hydrogen peroxide with its molarity.

 $ {{H}_{2}}{{O}_{2}}\to {{H}_{2}}O+\dfrac{1}{2}{{O}_{2}} $ 

According to the equation, 1 L of  $ {{H}_{2}}{{O}_{2}} $  will produce a V volume of oxygen gas.

Now, the volume of oxygen at STP is 22.7 L.

So, the moles of oxygen will be =  $ \dfrac{V}{22.7} $ 

According to the equation, 1 mole of $ {{H}_{2}}{{O}_{2}} $  produces half a mole of oxygen.

2 moles of  $ {{H}_{2}}{{O}_{2}} $  will produce 1 mole of oxygen.

So, the moles of  $ {{H}_{2}}{{O}_{2}} $  =  $ 2\text{ x }\dfrac{V}{22.7}=\dfrac{V}{11.35} $ 

Molarity will be  $ \dfrac{V}{11.35} $  (volume of hydrogen peroxide is 1 L)

So, Molarity =  $ \dfrac{V}{11.35} $ .


Note: So, by using the above equation the molarity of the hydrogen peroxide can easily be calculated when the volume strength of hydrogen peroxide is given. The volume strength of hydrogen peroxide at standard quantities is 5.6.