'x' g of NaCl is added to water in a beaker with a lid. The temperature of the system is raised from 1^circmathrmC$1^{\circ}\mathrm{C}$ to 25^circmathrmC$25^{\circ}\mathrm{C}$. Which out of the following plots, is best suited for the change in the molarity (M) of the solution with respect to temperature? [Consider the solubility of NaCl remains unchanged over the temperature range]

### Related Formula textMolarity (M) = fracn_textsoluteV_textsolution (mathrmL)$$\text{Molarity } (M) = \frac{n_{\text{solute}}}{V_{\text{solution}} (\mathrm{L})}$$ ### Core Logic Since solubility of mathrmNaCl$\mathrm{NaCl}$ remains unchanged, the number of dissolved moles of mathrmNaCl$\mathrm{NaCl}$ solute (n_textsolute$n_{\text{solute}}$) remains strictly constant. Thus, molarity M$M$ is strictly dependent on the volume of water (solvent) as temperature changes: M propto frac1V_textsolution$$M \propto \frac{1}{V_{\text{solution}}}$$ ### Step 1: Understand Water's Anomalous Expansion Water exhibits unique anomalous density behavior near freezing: - From 1^circmathrmC$1^{\circ}\mathrm{C}$ to 4^circmathrmC$4^{\circ}\mathrm{C}$, the density of water **increases** to a maximum. This contraction means the volume (V$V$) of water **decreases**. - From 4^circmathrmC$4^{\circ}\mathrm{C}$ to 25^circmathrmC$25^{\circ}\mathrm{C}$, the density of water **decreases** due to standard thermal expansion. Consequently, the volume (V$V$) **increases**. ### Step 2: Relate Volume to Molarity Because volume is in the denominator of the molarity equation: - From 1^circmathrmC$1^{\circ}\mathrm{C}$ to 4^circmathrmC$4^{\circ}\mathrm{C}$: Volume decreases implies$\implies$ Molarity **increases**. - At 4^circmathrmC$4^{\circ}\mathrm{C}$: Volume is minimum implies$\implies$ Molarity reaches a **maximum**. - From 4^circmathrmC$4^{\circ}\mathrm{C}$ to 25^circmathrmC$25^{\circ}\mathrm{C}$: Volume increases implies$\implies$ Molarity **decreases**. This behavior is perfectly represented by **Plot (2)**, which features a distinct peak around 4^circmathrmC$4^{\circ}\mathrm{C}$. ### Pattern Recognition Water is at its densest (and occupies minimum volume) at exactly 3.98^circmathrmC$3.98^\circ\mathrm{C}$ (4^circmathrmC$4^\circ\mathrm{C}$). Any concentration unit based on volume (such as Molarity or Normality) will reach a corresponding maximum at this temperature. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Chemistry: Solutions