To explore the relationship between the speeds of molecules in a process like diffusion, we can apply Graham's Law of Effusion, which states that the rate of effusion (or diffusion) of two gases is inversely proportional to the square root of their molar masses. This can also be used to compare the speeds of different gas molecules. The equation for Graham's law is:

$\frac{v_1}{v_2} = \sqrt{\frac{M_2}{M_1}}$

Where:

• $v_1$ and $v_2$ are the speeds of the gas molecules,
• $M_1$ and $M_2$ are the molar masses of the gases.

Step 1: Find the molar masses

• The molar mass of NH₃ (ammonia):

  • $M_1 = 14.01 + 3 \times 1.008 = 17.034 \, \text{g/mol}$.

• The molar mass of HCl (hydrogen chloride):

  • $M_2 = 1.008 + 35.45 = 36.458 \, \text{g/mol}$.

Step 2: Use Graham’s Law to find the speed ratio

Now, apply the values to the equation:

$\frac{v_{\text{NH}_3}}{v_{\text{HCl}}} = \sqrt{\frac{M_{\text{HCl}}}{M_{\text{NH}_3}}} = \sqrt{\frac{36.458}{17.034}} = \sqrt{2.14} \approx 1.46$

Conclusion:

The predicted ratio of the speeds of NH₃ to HCl molecules is approximately 1.46. This means that, under the same conditions, ammonia molecules (NH₃) move about 1.46 times faster than hydrogen chloride (HCl) molecules.

Would you like further details or explanations?

Here are five questions to deepen your understanding:

1. How does temperature affect the diffusion rates of NH₃ and HCl?
2. How would the diffusion ratio change if we considered a different pair of gases?
3. What assumptions are made in applying Graham’s law?
4. How does pressure impact the diffusion of gases?
5. What other factors might influence gas diffusion in real-life experiments?

Tip: Graham's law assumes ideal gas behavior, but real gases may deviate slightly due to intermolecular forces and non-ideal conditions.