NEET · Chemistry · STD 12 -1. Solution and colligative properties
Identify the correct statements:
A. The molality of 2.5 g of ethanoic acid (Molar mass : \(60 g mol ^{-1}\)) in 75 g of benzene solution is 0.556 m.
B. The molarity of a solution containing 5 g of NaOH (molar mass: \(40 g mol ^{-1}\)) 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 :
- A A, B and C only
- B A and B only
- C A and C only
- D A, D and E only
Answer & Solution
Correct Answer
(A) A, B and C only
Step-by-step Solution
Detailed explanation
(A) A, B and C only
Statement A : Molality is given by the number of moles of solute divided by the mass of solvent in kg.
Moles of ethanoic acid \(=\frac{2.5}{60}=\frac{1}{24} mol\)
Mass of benzene \(=75 g=0.075 kg\)
Molality \(=\frac{1 / 24}{0.075}=\frac{1000}{24 \times 75}=\frac{1000}{1800}=\frac{5}{9}=0.556 m\)
Statement A is correct.
Statement B : Molarity is given by the number of moles of solute divided by the volume of solution in litres.
Moles of NaOH \(=\frac{5}{40}=\frac{1}{8} mol\)
Volume of solution \(=450 mL=0.45 L\)
Molarity \(=\frac{1 / 8}{0.45}=\frac{1000}{8 \times 450}=\frac{1000}{3600}=\frac{5}{18}=0.278 M\)
Statement B is correct.
Statement C : The solubility of gases (like oxygen) in water increases with a decrease in temperature. Therefore, cold water contains more dissolved oxygen, making aquatic species more comfortable.
Statement C is correct.
Statement D : According to Henry's law, the solubility of a gas in a liquid is directly proportional to the pressure of the gas. Thus, solubility decreases with a decrease in pressure.
Statement D is incorrect.
Statement E : The mole fraction of component B is the ratio of the number of moles of B to the total number of moles in the mixture.
\(x_B=\frac{n_B}{n_A+n_B}\)
Statement E is incorrect.
Therefore, only statements A, B, and C are correct.
Statement A : Molality is given by the number of moles of solute divided by the mass of solvent in kg.
Moles of ethanoic acid \(=\frac{2.5}{60}=\frac{1}{24} mol\)
Mass of benzene \(=75 g=0.075 kg\)
Molality \(=\frac{1 / 24}{0.075}=\frac{1000}{24 \times 75}=\frac{1000}{1800}=\frac{5}{9}=0.556 m\)
Statement A is correct.
Statement B : Molarity is given by the number of moles of solute divided by the volume of solution in litres.
Moles of NaOH \(=\frac{5}{40}=\frac{1}{8} mol\)
Volume of solution \(=450 mL=0.45 L\)
Molarity \(=\frac{1 / 8}{0.45}=\frac{1000}{8 \times 450}=\frac{1000}{3600}=\frac{5}{18}=0.278 M\)
Statement B is correct.
Statement C : The solubility of gases (like oxygen) in water increases with a decrease in temperature. Therefore, cold water contains more dissolved oxygen, making aquatic species more comfortable.
Statement C is correct.
Statement D : According to Henry's law, the solubility of a gas in a liquid is directly proportional to the pressure of the gas. Thus, solubility decreases with a decrease in pressure.
Statement D is incorrect.
Statement E : The mole fraction of component B is the ratio of the number of moles of B to the total number of moles in the mixture.
\(x_B=\frac{n_B}{n_A+n_B}\)
Statement E is incorrect.
Therefore, only statements A, B, and C are correct.
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