Among the following, the intensive property is (properties are) — Electrochemistry Chemistry Question

💡 Solution & Explanation

Step 1 - Define Intensive and Extensive Properties In thermodynamics, physical properties of a chemical or physical system are broadly categorized into two types: 1. **Intensive Properties:** Properties that are independent of the size, mass, volume, or the quantity of matter present in the system. Examples include temperature ($T$), pressure ($P$), concentration ($C$), density ($\rho$), and specific heat capacity ($c$). 2. **Extensive Properties:** Properties whose values depend directly on the size, mass, volume, or the quantity of matter present in the system. Examples include mass ($m$), volume ($V$), total heat capacity ($C$), internal energy ($U$), enthalpy ($H$), and Gibbs free energy ($G$). A crucial rule governing these properties is that the ratio of two extensive properties is always an intensive property: $$\text{Intensive Property} = \frac{\text{Extensive Property}_1}{\text{Extensive Property}_2}$$ Step 2 - Analyze Option (A): Molar Conductivity ($\Lambda_m$) Conductivity ($\kappa$) is an intensive property because it is defined per unit volume. However, total conductance ($G$) of a solution is extensive because it depends on the cell dimensions and the amount of ions present. Molar conductivity ($\Lambda_m$) represents the conducting power of all the ions produced by dissolving one mole of an electrolyte in solution: $$\Lambda_m = \frac{\kappa}{C}$$ Since it is normalized per mole of electrolyte (by dividing the conductivity by molar concentration), it becomes independent of the total volume, size of the system, or quantity of the electrolyte used. Therefore, molar conductivity ($\Lambda_m$) is an **intensive property**. Step 3 - Analyze Option (B): Electromotive Force (EMF) The electromotive force (EMF) of a cell ($E_{\text{cell}}$) is the potential difference between its electrodes under zero-current conditions. The relationship between the standard Gibbs free energy change ($\Delta G^\circ$) and the standard cell potential ($E^\circ_{\text{cell}}$) is given by: $$\Delta G^\circ = -n F E^\circ_{\text{cell}} \implies E^\circ_{\text{cell}} = -\frac{\Delta G^\circ}{n F}$$ Where: * $\Delta G^\circ$ is the standard Gibbs free energy change, which is an **extensive property** (depends directly on the quantity of reactants). * $n$ is the number of moles of electrons transferred in the balanced stoichiometric equation, which is also an **extensive property** (scales with the stoichiometric coefficient). * $F$ is Faraday's constant ($F \approx 96500\text{ C mol}^{-1}$). Since $E^\circ_{\text{cell}}$ is proportional to the ratio of two extensive properties ($\Delta G^\circ / n$), it is independent of the size of the cell or the amount of substances undergoing reaction. For example, a tiny $1.5\text{ V}$ battery and a giant $1.5\text{ V}$ battery of the same chemical composition deliver the same voltage. Therefore, EMF is an **intensive property**. Step 4 - Analyze Option (C): Resistance ($R$) The electrical resistance ($R$) of a conductor is determined by its resistivity ($\rho$) and its physical dimensions: $$R = \rho \frac{l}{A}$$ Where: * $l$ is the length of the conductor (extensive). * $A$ is the cross-sectional area of the conductor (extensive). If the physical size of the conductor changes (for example, if we double its length), the resistance changes. Because resistance scales with the size of the physical system, it is an **extensive property**. Step 5 - Analyze Option (D): Heat Capacity ($C$) The heat capacity ($C$) of a substance is the quantity of heat required to raise its temperature by $1^\circ\text{C}$ (or $1\text{ K}$): $$C = \frac{q}{\Delta T} = m \cdot c$$ Where: * $m$ is the mass of the substance (extensive). * $c$ is the specific heat capacity (intensive). Since the total heat capacity ($C$) is directly proportional to the mass ($m$) of the sample present in the system, it scales with the size of the system. Therefore, heat capacity is an **extensive property**. Step 6 - Conclusion and Identification of Correct Options * **Molar conductivity:** Intensive property (Correct) * **Electromotive force:** Intensive property (Correct) * **Resistance:** Extensive property (Incorrect) * **Heat capacity:** Extensive property (Incorrect) $$\text{Correct Options: } \boxed{\text{A, B}}$$