chemistry : class11 Pressure Dependence of Surface Tension : Surface tension : States of Matter: Gases and Liquids MCQ Questions and Answers
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Pressure Dependence of Surface Tension
MCQ questions and answers.
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MCQ Questions
1. At constant temperature, the surface tension of a liquid is experimentally found to vary with pressure according to γ = 72.0 + 0.020(P − 1.0) mN m⁻¹, where P is in bar. What is the surface tension at 6.0 bar?
A.
72.02 mN m⁻¹
B.
72.10 mN m⁻¹
C.
72.12 mN m⁻¹
D.
72.20 mN m⁻¹
Correct Answer:
72.10 mN m⁻¹
Explanation:
Using γ = 72.0 + 0.020(6.0 − 1.0), γ = 72.0 + 0.10 = 72.10 mN m⁻¹. The positive coefficient shows that surface tension increases with pressure at constant temperature.
2. For a liquid at constant temperature, dγ/dP = −0.015 mN m⁻¹ bar⁻¹. If its surface tension is 58.0 mN m⁻¹ at 2 bar, what will it be at 12 bar, assuming the dependence remains linear?
A.
57.15 mN m⁻¹
B.
57.85 mN m⁻¹
C.
58.15 mN m⁻¹
D.
58.85 mN m⁻¹
Correct Answer:
57.85 mN m⁻¹
Explanation:
The pressure change is 10 bar. Thus, Δγ = (−0.015)(10) = −0.15 mN m⁻¹, and γ = 58.0 − 0.15 = 57.85 mN m⁻¹. The negative derivative indicates a decrease in surface tension with pressure.
3. Two liquids have pressure coefficients of surface tension at the same temperature: (dγ/dP)₁ = 0.012 mN m⁻¹ bar⁻¹ and (dγ/dP)₂ = 0.030 mN m⁻¹ bar⁻¹. If their initial surface tensions are equal, which liquid shows the larger increase in surface tension when pressure is raised by 25 bar?
A.
Liquid 1, by 0.30 mN m⁻¹
B.
Liquid 2, by 0.30 mN m⁻¹
C.
Liquid 1, by 0.75 mN m⁻¹
D.
Liquid 2, by 0.75 mN m⁻¹
Correct Answer:
Liquid 2, by 0.75 mN m⁻¹
Explanation:
For liquid 2, Δγ = (0.030)(25) = 0.75 mN m⁻¹. For liquid 1, the increase is only (0.012)(25) = 0.30 mN m⁻¹. Therefore liquid 2 has the larger pressure-induced increase.
4. A liquid has γ = 64.0 mN m⁻¹ at 1 bar and γ = 64.36 mN m⁻¹ at 13 bar at constant temperature. What is its average pressure coefficient of surface tension?
A.
0.003 mN m⁻¹ bar⁻¹
B.
0.030 mN m⁻¹ bar⁻¹
C.
0.300 mN m⁻¹ bar⁻¹
D.
3.00 mN m⁻¹ bar⁻¹
Correct Answer:
0.030 mN m⁻¹ bar⁻¹
Explanation:
The average coefficient is Δγ/ΔP = (64.36 − 64.0)/(13 − 1) = 0.36/12 = 0.030 mN m⁻¹ bar⁻¹. Its positive value indicates an increase of surface tension with pressure over this range.
5. At a particular temperature, the surface tension of a liquid is represented by γ(P) = 50.0 + 0.040P − 0.00050P² mN m⁻¹, with P in bar. At which pressure is the surface tension maximum within the physically relevant positive-pressure range?
A.
20 bar
B.
40 bar
C.
60 bar
D.
80 bar
Correct Answer:
40 bar
Explanation:
The pressure coefficient is dγ/dP = 0.040 − 0.00100P. Setting it equal to zero gives P = 40 bar. Since the coefficient changes from positive to negative there, surface tension is maximum at 40 bar.
6. For γ(P) = 68.0 + 0.010P − 0.00020P² mN m⁻¹, at which pressure does the surface tension stop increasing with pressure?
A.
10 bar
B.
25 bar
C.
50 bar
D.
100 bar
Correct Answer:
25 bar
Explanation:
Differentiating gives dγ/dP = 0.010 − 0.00040P. The surface tension stops increasing when this derivative becomes zero: P = 0.010/0.00040 = 25 bar.
7. A liquid has a pressure dependence γ = 75.0 + 0.025(P − 1.0) mN m⁻¹ at constant temperature. By how much must the pressure increase to raise its surface tension by 0.50 mN m⁻¹?
A.
5 bar
B.
10 bar
C.
20 bar
D.
50 bar
Correct Answer:
20 bar
Explanation:
For a linear dependence, Δγ = (dγ/dP)ΔP. Therefore, ΔP = 0.50/0.025 = 20 bar. The required pressure increase is independent of the reference pressure in this relation.
8. At constant temperature, the surface tension changes from 40.0 to 40.8 mN m⁻¹ when pressure changes from 5 to 45 bar. Assuming a linear dependence, what surface tension is expected at 30 bar?
A.
40.30 mN m⁻¹
B.
40.40 mN m⁻¹
C.
40.50 mN m⁻¹
D.
40.60 mN m⁻¹
Correct Answer:
40.50 mN m⁻¹
Explanation:
The pressure coefficient is (40.8 − 40.0)/(45 − 5) = 0.8/40 = 0.020 mN m⁻¹ bar⁻¹. At 30 bar, the pressure increase from 5 bar is 25 bar, so γ = 40.0 + (0.020)(25) = 40.50 mN m⁻¹.
9. For a liquid whose surface tension increases linearly with pressure, which statement correctly distinguishes pressure dependence of surface tension from the Laplace pressure of a curved interface?
A.
Laplace pressure is the intrinsic surface tension, whereas pressure dependence describes curvature.
B.
Pressure dependence describes how γ changes with pressure, whereas Laplace pressure is a pressure difference produced by curvature and γ.
C.
Both terms always represent the same quantity and have identical units.
D.
Pressure dependence can occur only in gas bubbles, whereas Laplace pressure can occur only in liquid drops.
Correct Answer:
Pressure dependence describes how γ changes with pressure, whereas Laplace pressure is a pressure difference produced by curvature and γ.
Explanation:
The pressure coefficient dγ/dP describes the change in surface tension when the pressure changes. Laplace pressure, in contrast, is the pressure difference across a curved interface, determined by surface tension and curvature; the two concepts are related but not identical.
10. For a liquid at fixed temperature, γ = 60.0 mN m⁻¹ at 2 bar and dγ/dP = 0.018 mN m⁻¹ bar⁻¹. A pressure increase of 15 bar is then followed by a pressure decrease of 5 bar. Assuming the same linear relation throughout, what is the final surface tension?
A.
60.18 mN m⁻¹
B.
60.27 mN m⁻¹
C.
60.36 mN m⁻¹
D.
60.45 mN m⁻¹
Correct Answer:
60.18 mN m⁻¹
Explanation:
The net pressure change is +15 − 5 = +10 bar. Hence, Δγ = (0.018)(10) = 0.18 mN m⁻¹, giving a final surface tension of 60.18 mN m⁻¹. Under a reversible linear dependence, only the net pressure change matters.
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