Select the smaller member of each pair.
$N$ or $N^{3}$
$\mathrm{N}$
$$
N^{3}
$$

Question

Accepted Answer

Sure, let's address the questions one by one. ### Question 1: Calculating the Diffusion Current for a $1 \, ext{mM}$ Solution of $Ti^{+}$ ∻Solution∻ ‖ 1 ⋮ **Identify the given data**: The concentration of $Ti^{+}$ is $1 \, ext{mM}$, and the diffusion coefficients for $Ti^{+}$ and $Cd^{2+}$ are provided. ‖ ‖ 2 ⋮ **Use the Nernst-Einstein equation**: The diffusion current $I_d$ can be calculated using the equation $I_d = n F D \frac{dC}{dx}$, where $n$ is the number of electrons, $F$ is the Faraday constant, $D$ is the diffusion coefficient, and $\frac{dC}{dx}$ is the concentration gradient. ‖ ‖ 3 ⋮ **Substitute the values**: Assuming a linear concentration gradient, substitute the given values into the equation to find the diffusion current. ‖ ∻Answer∻ ⚹ The diffusion current for a $1 \, ext{mM}$ solution of $Ti^{+}$ is calculated using the Nernst-Einstein equation. ⚹ ### Question 2: Determining the Mass of Methanol Required for Preparing a Solution ∻Solution∻ ‖ 1 ⋮ **Identify the target concentration and volume**: Determine the desired concentration and volume of the methanol solution. ‖ ‖ 2 ⋮ **Use the formula**: The mass of methanol required can be calculated using $m = C imes V imes M$, where $C$ is the concentration, $V$ is the volume, and $M$ is the molar mass of methanol. ‖ ‖ 3 ⋮ **Substitute the values**: Substitute the given concentration, volume, and molar mass of methanol into the formula to find the mass. ‖ ∻Answer∻ ⚹ The mass of methanol required for preparing the solution is calculated using the formula $m = C imes V imes M$. ⚹ ### Question 3: Maximum Number of a Compound to Undergo Electrophilic Aromatic Substitution Reaction ∻Solution∻ ‖ 1 ⋮ **Identify the compound**: Determine the structure of the compound and the positions available for substitution. ‖ ‖ 2 ⋮ **Consider the substituents**: Analyze the effect of existing substituents on the aromatic ring and their directing effects. ‖ ‖ 3 ⋮ **Determine the maximum number**: Based on the structure and substituents, determine the maximum number of positions available for electrophilic aromatic substitution. ‖ ∻Answer∻ ⚹ The maximum number of a compound to undergo electrophilic aromatic substitution reaction depends on the structure and substituents of the aromatic ring. ⚹ ### Question 4: Best Electrical Conductor Among Different Solutions ∻Solution∻ ‖ 1 ⋮ **Identify the solutions**: List the different solutions provided. ‖ ‖ 2 ⋮ **Compare conductivity**: Compare the ionic strength and mobility of ions in each solution. ‖ ‖ 3 ⋮ **Determine the best conductor**: The solution with the highest ionic strength and mobility will be the best electrical conductor. ‖ ∻Answer∻ ⚹ The best electrical conductor among different solutions is determined by comparing their ionic strength and mobility. ⚹ ### Question 5: Calculating the Concentration of a New Solution Formed by Mixing Two Solutions of Calcium Nitrate ∻Solution∻ ‖ 1 ⋮ **Identify the concentrations and volumes**: Determine the concentrations and volumes of the two calcium nitrate solutions being mixed. ‖ ‖ 2 ⋮ **Use the dilution formula**: The concentration of the new solution can be calculated using $C_{ ext{new}} = \frac{C_1V_1 + C_2V_2}{V_1 + V_2}$, where $C_1$ and $C_2$ are the initial concentrations, and $V_1$ and $V_2$ are the volumes. ‖ ‖ 3 ⋮ **Substitute the values**: Substitute the given concentrations and volumes into the formula to find the new concentration. ‖ ∻Answer∻ ⚹ The concentration of the new solution formed by mixing two solutions of calcium nitrate is calculated using the dilution formula. ⚹ ### Question 6: Finding the Diffusion Coefficient of $Cd^{2+}$ Ion Based on Given Data ∻Solution∻ ‖ 1 ⋮ **Identify the given data**: Determine the data provided for the $Cd^{2+}$ ion. ‖ ‖ 2 ⋮ **Use the appropriate equation**: The diffusion coefficient can be calculated using the Stokes-Einstein equation $D = \frac{k_B T}{6 \pi \eta r}$, where $k_B$ is the Boltzmann constant, $T$ is the temperature, $\eta$ is the viscosity, and $r$ is the radius of the ion. ‖ ‖ 3 ⋮ **Substitute the values**: Substitute the given data into the equation to find the diffusion coefficient. ‖ ∻Answer∻ ⚹ The diffusion coefficient of $Cd^{2+}$ ion is calculated using the Stokes-Einstein equation. ⚹ ### Summary ∻Key Concept∻ ⚹ The key concept involves using specific equations and formulas to calculate diffusion current, mass of methanol, maximum number of substitutions, electrical conductivity, concentration of mixed solutions, and diffusion coefficients. ⚹ ∻Explanation∻ ⚹ Each calculation requires identifying the given data, using the appropriate formula, and substituting the values to find the desired result. ⚹◊What is the significance of comparing the expressions $N$ and $N^{3}$ in terms of their values in Chemistry?⍭ Generate me a similar question◊

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