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Oxygen crosses the same distance about 18,000 times faster in air than in water.
Its diffusion coefficient is 1.8 × 10−5 m2/s in air but 1.0 × 10−9 m2/s in water. In a gas, O₂ travels far between collisions; in a liquid it bumps a neighbor at almost every step.
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Cotton plugs soaked in concentrated aqueous NH₃ and in concentrated HCl are placed at the same moment at opposite ends of a 1.00-m glass tube. NH₃(g) (17.0 g/mol) and HCl(g) (36.5 g/mol) move along the tube, and a ring of solid NH₄Cl forms where they meet. If both gases move as Graham's law predicts, about how far from the NH₃ end does the ring form?
Pick one. The red pen does the rest.
The deciding lineBy Graham's law, the rates at which two gases effuse or spread at the same temperature are inversely proportional to the square roots of their molar masses.
Why C: rate(NH₃)/rate(HCl) = √(36.5/17.0) = 1.47. In the same time NH₃ covers 1.47 parts of the distance for every 1 part covered by HCl, so the ring forms 1.47/2.47 × 100 cm = 59 cm from the NH₃ end.
Why each choice fails
ADirection reversed: 41 cm is the distance from the HCl end; NH₃ is the lighter gas and moves faster, so it covers the longer stretch, 59 cm.
BLook-alike terms: at the same temperature the molecules share the same average kinetic energy, not the same speed; NH₃ moves √(36.5/17.0) = 1.47 times as fast as HCl.
CHolds: NH₃ moves √(36.5/17.0) = 1.47 times as fast as HCl, so it covers 1.47/(1 + 1.47) = 0.59 of the 1.00-m tube.
DScale slip: 68 cm uses the mass ratio, 36.5/17.0 = 2.15, as the speed ratio; Graham's law takes its square root, 1.47, which gives 59 cm.
A balloon is filled with equal moles of helium (4.0 g/mol) and nitrogen (28.0 g/mol) at the same temperature. Through a tiny leak, how does the rate of effusion of helium compare with that of nitrogen?
Pick one. The red pen does the rest.
The deciding lineGraham's law: the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
Why B: rate(He)/rate(N₂) = √(28.0/4.0) = √7 ≈ 2.6: helium effuses about 2.6 times faster.
Why each choice fails
AOne step short: 7 is the ratio of the molar masses; the rates go as the square root.
BHolds: √7 ≈ 2.6.
CDirection reversed: the lighter gas effuses faster.
DConditions ignored: equal moles and temperature do not make the rates equal; molar mass sets the speed.
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