A. The molality of a 2.5 g of ethanoic acid (Molar mass : $60 \text{ g mol}^{-1}$) in 75 g of benzene solution is $0.556 \text{ m}$.
B. The molarity of a solution containing 5 g of NaOH (molar mass : $40 \text{ g mol}^{-1}$) in 450 mL of solution is 0.278 M at 298 K.
C. Aquatic species are more comfortable in cold water.
D. The solubility of gas increases with decrease in pressure.
E. For a binary mixture of A and B, the number of moles of A and B are $n_A$ and $n_B$ respectively, the mole fraction of B will be $x_B = \frac{n_A}{n_A + n_B}$.
Choose the correct answer from the options given below :
Statement A Analysis: Molality Calculation
To verify statement A, we calculate the molality of the ethanoic acid solution.
- Mass of solute (ethanoic acid) = 2.5 g
- Molar mass of solute = $60 \text{ g mol}^{-1}$
- Mass of solvent (benzene) = 75 g = 0.075 kg
- Moles of solute = $\frac{\text{Mass of solute}}{\text{Molar mass of solute}} = \frac{2.5 \text{ g}}{60 \text{ g mol}^{-1}} \approx 0.04167 \text{ mol}$
- Molality ($m$) = $\frac{\text{Moles of solute}}{\text{Mass of solvent (kg)}} = \frac{0.04167 \text{ mol}}{0.075 \text{ kg}} \approx 0.5556 \text{ m}$
The calculated molality is approximately $0.556 \text{ m}$, making statement A correct.
Statement B Analysis: Molarity Calculation
To verify statement B, we calculate the molarity of the NaOH solution.
- Mass of solute (NaOH) = 5 g
- Molar mass of solute = $40 \text{ g mol}^{-1}$
- Volume of solution = 450 mL = 0.450 L
- Moles of solute = $\frac{\text{Mass of solute}}{\text{Molar mass of solute}} = \frac{5 \text{ g}}{40 \text{ g mol}^{-1}} = 0.125 \text{ mol}$
- Molarity ($M$) = $\frac{\text{Moles of solute}}{\text{Volume of solution (L)}} = \frac{0.125 \text{ mol}}{0.450 \text{ L}} \approx 0.2778 \text{ M}$
The calculated molarity is approximately $0.278 \text{ M}$, making statement B correct.
Statement C Analysis: Aquatic Life Comfort
The solubility of gases in water is temperature-dependent. Gases are more soluble in colder water than in warmer water. Aquatic species, like fish, require dissolved oxygen, which is more abundant in cold water. Therefore, aquatic species are more comfortable in cold water.
Statement C is correct.
Statement D Analysis: Gas Solubility vs Pressure
According to Henry's Law, the solubility of a gas in a liquid is directly proportional to the partial pressure of that gas above the liquid. This means solubility increases with increasing pressure.
Statement D, which claims solubility increases with decreasing pressure, is incorrect.
Statement E Analysis: Mole Fraction Formula
For a binary mixture of components A and B, with moles $n_A$ and $n_B$ respectively:
- Total moles = $n_A + n_B$
- The mole fraction of B ($x_B$) is defined as: $x_B = \frac{n_B}{n_A + n_B}$
- The formula provided in the statement, $x_B = \frac{n_A}{n_A + n_B}$, actually represents the mole fraction of A ($x_A$).
Statement E is incorrect.
Conclusion
Based on the analysis, the correct statements are A, B, and C.
Therefore, the correct option is A, B and C only.
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Consider the above reaction, what mass of $CaCl_2$ will be formed if 250 mL of 0.76 M HCl reacts with 1000 g of $CaCO_3$ ?
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