Answer
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Hint: For this question, we need to find the value of ${E^0}$for the half cell reaction in Volts and then by equating it to the value given; we can find out the value of x.
We have the formula for finding Standard emf of the cell is :
$E_{{I^ - }|AgI|Ag}^0 = E_{A{g^ + }|Ag}^0 + 0.0592\log {K_{sp}}$
Using this formula, we can calculate the value in volts and then equate the value to the given, the value of x will come.
Complete step by step answer :
For such numerical type questions, first let us write what is given to us and what we need to find out. We have the reaction for the cell is as -
$AgI + {e^ - } \to Ag + {I^ - }$
Given :
$p{K_{sp}}$of AgI solution = 16.07
${E^0}$( $A{g^ + }/Ag$) = 0.7991 V
${E^0}$for the half cell reaction $AgI + {e^ - } \to Ag + {I^ - }$= 149 $ \times {10^{ - x}}$V
To find : The value of x
We know that $p{K_{sp}}$= - log ${K_{sp}}$
We have the formula for finding Standard emf of the cell is :
$E_{{I^ - }|AgI|Ag}^0 = E_{A{g^ + }|Ag}^0 + 0.0592\log {K_{sp}}$
On filling the values in above formula, we can find the value -
\[E_{{I^ - }|AgI|Ag}^0 = 0.7991 - 0.0592 \times 16.07\]
\[E_{{I^ - }|AgI|Ag}^0\]= - 0.149 V
From the question, we have value 149 $ \times {10^{ - x}}$.
So, by equating we can find out the value of ‘x’ as -
149 $ \times {10^{ - x}}$ = - 0.149 V
149 $ \times {10^{ - x}}$ = 149 $ \times {10^{ - 3}}$
Thus, the value of ‘x’ comes out to be 3.
Note: It must be noted that when we remove points. This means we have multiplied by 1000 on the right-hand side and we have to equally divide by 1000 to get the same value. The value ${10^{ - 3}}$ means division by 1000. The negative sign in the power of numerator means when we will get that value to the denominator, the value will become positive.
We have the formula for finding Standard emf of the cell is :
$E_{{I^ - }|AgI|Ag}^0 = E_{A{g^ + }|Ag}^0 + 0.0592\log {K_{sp}}$
Using this formula, we can calculate the value in volts and then equate the value to the given, the value of x will come.
Complete step by step answer :
For such numerical type questions, first let us write what is given to us and what we need to find out. We have the reaction for the cell is as -
$AgI + {e^ - } \to Ag + {I^ - }$
Given :
$p{K_{sp}}$of AgI solution = 16.07
${E^0}$( $A{g^ + }/Ag$) = 0.7991 V
${E^0}$for the half cell reaction $AgI + {e^ - } \to Ag + {I^ - }$= 149 $ \times {10^{ - x}}$V
To find : The value of x
We know that $p{K_{sp}}$= - log ${K_{sp}}$
We have the formula for finding Standard emf of the cell is :
$E_{{I^ - }|AgI|Ag}^0 = E_{A{g^ + }|Ag}^0 + 0.0592\log {K_{sp}}$
On filling the values in above formula, we can find the value -
\[E_{{I^ - }|AgI|Ag}^0 = 0.7991 - 0.0592 \times 16.07\]
\[E_{{I^ - }|AgI|Ag}^0\]= - 0.149 V
From the question, we have value 149 $ \times {10^{ - x}}$.
So, by equating we can find out the value of ‘x’ as -
149 $ \times {10^{ - x}}$ = - 0.149 V
149 $ \times {10^{ - x}}$ = 149 $ \times {10^{ - 3}}$
Thus, the value of ‘x’ comes out to be 3.
Note: It must be noted that when we remove points. This means we have multiplied by 1000 on the right-hand side and we have to equally divide by 1000 to get the same value. The value ${10^{ - 3}}$ means division by 1000. The negative sign in the power of numerator means when we will get that value to the denominator, the value will become positive.
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