Graham's Law of Effusion: Worked Examples and Problem-Solving

🧪 Quick Study Guide

• ⚖️ Graham's Law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
• ➗ Mathematically, it's expressed as: $\frac{Rate_1}{Rate_2} = \sqrt{\frac{M_2}{M_1}}$, where $Rate_1$ and $Rate_2$ are the rates of effusion of gas 1 and gas 2, and $M_1$ and $M_2$ are their respective molar masses.
• 💨 Effusion is the process where a gas escapes through a tiny hole into a vacuum.
• 🌡️ Temperature affects the rate of effusion. Ensure temperature is constant or accounted for in calculations.
• 🔢 Molar mass is typically expressed in grams per mole (g/mol).
• 💡 Remember to square the rates or square root the molar masses when applying the formula.
• 📝 Units for rate must be consistent (e.g., molecules per second, volume per minute).

✍️ Practice Quiz

1. What does Graham's Law describe?
   1. (A) The rate of diffusion of a liquid
   2. (B) The rate of effusion of a gas
   3. (C) The rate of reaction of a solid
   4. (D) The rate of dissolving of a salt
2. If gas A has a molar mass of 16 g/mol and gas B has a molar mass of 36 g/mol, what is the ratio of their rates of effusion (Rate A / Rate B)?
   1. (A) 1.5
   2. (B) 0.67
   3. (C) 2.25
   4. (D) 0.44
3. Which gas will effuse faster: Hydrogen (H₂) or Oxygen (O₂)?
   1. (A) Hydrogen
   2. (B) Oxygen
   3. (C) They will effuse at the same rate
   4. (D) Cannot be determined
4. A gas effuses at a rate of 4.0 mol/min. Another gas, with a molar mass twice as large, will effuse at approximately what rate?
   1. (A) 8.0 mol/min
   2. (B) 2.8 mol/min
   3. (C) 2.0 mol/min
   4. (D) 5.7 mol/min
5. What is the molar mass of a gas that effuses twice as fast as $SO_2$ (64 g/mol)?
   1. (A) 16 g/mol
   2. (B) 32 g/mol
   3. (C) 128 g/mol
   4. (D) 256 g/mol
6. If two gases are at the same temperature, which property primarily determines their rate of effusion?
   1. (A) Pressure
   2. (B) Volume
   3. (C) Molar Mass
   4. (D) Density
7. A gas effuses through an opening in 30 seconds. If a different gas takes 60 seconds to effuse through the same opening under the same conditions, what is the ratio of the molar mass of the second gas to the first gas?
   1. (A) 1:2
   2. (B) 2:1
   3. (C) 1:4
   4. (D) 4:1