To calculate the overall standard reduction potential for a series of redox reac tions, use the relationship \(∆G = −nFE^◦\) and combine the contributions from all steps.
The reactions are as follows:
The total Gibbs free energy for the combined reaction is:
\[ \Delta G_3 = \Delta G_1 + \Delta G_2 \]
Substitute \( \Delta G = -nFE^\circ \):
\[ -4FE^\circ_3 = -3F(2.2) + (-1F)(0.7) \]
Simplify the equation:
\[ 4E^\circ_3 = 6.6 + 0.7 = 7.3 \]
Divide by 4:
\[ E^\circ_3 = \frac{7.3}{4} = 1.825 \, \text{V} \]
Express in millivolts:
\[ E^\circ_3 = 1.825 \times 10^3 \, \text{mV} \]
The value of \( x \) is 1825.
Let \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32