Answer
Verified
394.8k+ views
Hint: In order to find the value of x, we apply the Nernst equation. The Nernst equation provides a relation between the cell potential, the standard cell potential, the reaction quotient and the temperature.
Complete answer:
Let us move to the given question.
In the Cathode:
\[A{g^ + } + {e^ - } \to Ag,{\text{ E}}_{\dfrac{{A{g^ + }}}{{Ag}}}^o = 0.8V\]
In the anode:
\[\dfrac{1}{2}{H_2} \to {H^ + } + {e^ - },{\text{ E}}_{\dfrac{{{H_2}}}{{{H^ + }}}}^o = 0V\]
The net equation is
\[A{g^ + } + \dfrac{1}{2}{H_2} \to Ag + {H^ + }\]
Now we have to use the Nernst equation. Let us first understand what a Nernst equation is. The Nernst equation provides a relation between the cell potential, the standard cell potential, the reaction quotient and the temperature. The Nernst equation is an equation which is mostly used to calculate the cell potential of the electrochemical cell at any given conditions like temperature, pressure and reactant concentration.
The Nernst equation at \[25^\circ C\]is given as
\[{E_{Cell}} = E_{Cell}^o - \dfrac{{0.0591}}{1}\log \dfrac{{[{H^ + }]}}{{[A{g^ + }]}}\]
pH is given as 5.03.
\[pH = 5.03 = - \log [{H^ + }]\]
\[[{H^ + }] = {10^{ - 5.03}}\]
\[1.0 = 0.8 - \dfrac{{0.0591}}{1}\log \dfrac{{[{{10}^{ - 5.03}}]}}{{[x]}}\]
\[0.224 = 5.03 \times 0.0591 + 0.0591\log [x]\]
By solving it we get
\[[x] = 2 \times {10^{ - 2}}M\]
The value of x is \[2 \times {10^{ - 2}}M\].
Hence the correct answer is option (A) \[2 \times {10^{ - 2}}M\]
Note:
We have to remember that the Nernst equation can be used to calculate the following:
- Electromotive force of an electrochemical cell
- Unknown ionic concentration
- pH of the solution
- Solubility of the sparingly soluble salt can be measured.
- Standard electrode potential
- Single electrode oxidation or reduction potential at various conditions.
Complete answer:
Let us move to the given question.
In the Cathode:
\[A{g^ + } + {e^ - } \to Ag,{\text{ E}}_{\dfrac{{A{g^ + }}}{{Ag}}}^o = 0.8V\]
In the anode:
\[\dfrac{1}{2}{H_2} \to {H^ + } + {e^ - },{\text{ E}}_{\dfrac{{{H_2}}}{{{H^ + }}}}^o = 0V\]
The net equation is
\[A{g^ + } + \dfrac{1}{2}{H_2} \to Ag + {H^ + }\]
Now we have to use the Nernst equation. Let us first understand what a Nernst equation is. The Nernst equation provides a relation between the cell potential, the standard cell potential, the reaction quotient and the temperature. The Nernst equation is an equation which is mostly used to calculate the cell potential of the electrochemical cell at any given conditions like temperature, pressure and reactant concentration.
The Nernst equation at \[25^\circ C\]is given as
\[{E_{Cell}} = E_{Cell}^o - \dfrac{{0.0591}}{1}\log \dfrac{{[{H^ + }]}}{{[A{g^ + }]}}\]
pH is given as 5.03.
\[pH = 5.03 = - \log [{H^ + }]\]
\[[{H^ + }] = {10^{ - 5.03}}\]
\[1.0 = 0.8 - \dfrac{{0.0591}}{1}\log \dfrac{{[{{10}^{ - 5.03}}]}}{{[x]}}\]
\[0.224 = 5.03 \times 0.0591 + 0.0591\log [x]\]
By solving it we get
\[[x] = 2 \times {10^{ - 2}}M\]
The value of x is \[2 \times {10^{ - 2}}M\].
Hence the correct answer is option (A) \[2 \times {10^{ - 2}}M\]
Note:
We have to remember that the Nernst equation can be used to calculate the following:
- Electromotive force of an electrochemical cell
- Unknown ionic concentration
- pH of the solution
- Solubility of the sparingly soluble salt can be measured.
- Standard electrode potential
- Single electrode oxidation or reduction potential at various conditions.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Which are the Top 10 Largest Countries of the World?
One cusec is equal to how many liters class 8 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
The mountain range which stretches from Gujarat in class 10 social science CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths