Question

When an aqueous solution of sodium ethanoate is electrolyzed, the volume of gas obtained at cathode at a pressure of 1.0 bar and 298K temperature when 2.0 Faraday of electricity is passed is;
A. 67.2 litres
B. 68.1 litres
C. 73.2 litres
D. 24.43 litres

Answer 1

Hint: The conditions of the reaction are at standard temperature-pressure (i.e., 1 bar pressure and 298K). Therefore, we can use the concept that 1 mole of any gas at STP has 22.4 L volume, to get the desired answer.

Complete answer:
To get the number of moles of gas evolved we need to see the chemical reaction. Therefore first, we will write the chemical reaction of sodium ethanoate being ionized( forming corresponding ions).
 $ {\text{C}}{{\text{H}}_{\text{3}}}{\text{COONa}}\xrightarrow{{{{\text{H}}_{\text{2}}}{\text{O}}}}{\text{C}}{{\text{H}}_3}{\text{CO}}{{\text{O}}^ - } + {\text{N}}{{\text{a}}^{\text{ + }}} $
The gas evolved will be carbon dioxide ( $ {\text{C}}{{\text{O}}_{\text{2}}} $ ) and ethane ( $ {\text{C}}{{\text{H}}_{\text{3}}} - {\text{C}}{{\text{H}}_{\text{3}}} $ ) from $ {\text{C}}{{\text{H}}_3}{\text{CO}}{{\text{O}}^ - } $ and the reaction could be written as;
 $ {\text{2C}}{{\text{H}}_{\text{3}}}{\text{CO}}{{\text{O}}^ - } \to {\text{2C}}{{\text{O}}_{\text{2}}}{\text{ + C}}{{\text{H}}_{\text{3}}} - {\text{C}}{{\text{H}}_{\text{3}}} $
From the balanced reaction, we can say that for 2F of electricity passed, we get 3 moles of gas i.e., 2 moles of $ {\text{C}}{{\text{O}}_{\text{2}}} $ and 1 mole of $ {\text{C}}{{\text{H}}_{\text{3}}} - {\text{C}}{{\text{H}}_{\text{3}}} $
Using the concept of 1 mole of gas at STP = 22.4 L, we can write that;
 $ \Rightarrow $ 3 moles of gas = 22.4 $ \times $ 3 L = 67.2 L

Hence, the correct answer is option (A) i.e., 67.2 L of gas will be evolved.

Note:
There is another method to calculate the number of moles, using molarity, but since we are not given the mass number of solute used. We did not use the molarity formula. Also, the options are given in litre if they were given in mL, we then had to change the S.I unit. Hence, pay attention to the S.I units of the physical quantity.