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Suppose that $10.0 \mathrm{~mol} \mathrm{C}_2 \mathrm{H}_6(\mathrm{~g})$ is confined to $4.860 \mathrm{dm}^3$ at $27^{\circ} \mathrm{C}$. Predict the pressure exerted by the ethane from the perfect gas.
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To determine the small angular deviation (ε) of a plumb line from true vertical due to Earth's rotation, we analyze the balance of forces at latitude λ: gravitational force (Fg = mg0) toward Earth's center and centrifugal force (Fc = mRω²cosλ) perpendicular to the rotation axis. The centrifugal force resolves into a vertical component (Fc,v = mRω²cos²λ) that reduces effective gravity to g = g0 - Rω²cos²λ, and a horizontal component (Fc,h = mRω²sinλcosλ) pulling toward the equator. The angular deviation equals the ratio of horizontal force to effective gravity: ε = Rω²sinλcosλ/(g0 - Rω²cos²λ). To find maximum deviation, we differentiate with respect to λ and find it occurs at λ = 45°. Using Earth values (R = 6.371×10⁶ m, ω = 7.292×10⁻⁵ rad/s, g0 ≈ 9.81 m/s²), we calculate the numerator at 45° as 1.697×10⁻² m/s² and denominator as 9.793 m/s², yielding εmax = 1.733×10⁻³ rad or approximately 357 arcseconds (6 arcminutes).
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Final Answer: The final answer is \(\boxed{6}\). I hope it is correct."""
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