Which is the theoretical effusion of NH3 and the theoretical effusion of HCl?
The rate of effusion is proportional to 1/(square root of the molar mass).
To determine the theoretical effusion rates of NH3 (ammonia) and HCl (hydrochloric acid), we need to compare their molar masses and calculate the ratio based on the given relationship: "The rate of effusion is proportional to 1/(square root of the molar mass)."
Here are the steps to find the theoretical effusion rates:
1. Identify the molar mass:
- Molar mass of NH3 (ammonia): Nitrogen (N) has an atomic mass of approximately 14.01 g/mol, and Hydrogen (H) has an atomic mass of approximately 1.01 g/mol. NH3 consists of 1 nitrogen atom and 3 hydrogen atoms.
Molar mass of NH3 = (1 * 14.01 g/mol) + (3 * 1.01 g/mol) = 17.04 g/mol
- Molar mass of HCl (hydrochloric acid): Hydrogen (H) has an atomic mass of approximately 1.01 g/mol, and Chlorine (Cl) has an atomic mass of approximately 35.45 g/mol. HCl consists of 1 hydrogen atom and 1 chlorine atom.
Molar mass of HCl = 1.01 g/mol + 35.45 g/mol = 36.46 g/mol
2. Calculate the ratio of the inverse square roots of the molar masses:
- Ratio = (1/sqrt(Molar mass of NH3)) / (1/sqrt(Molar mass of HCl))
- Ratio = sqrt(Molar mass of HCl) / sqrt(Molar mass of NH3)
- Ratio = sqrt(36.46 g/mol) / sqrt(17.04 g/mol)
- Ratio = 6.04 g/mol / 4.13 g/mol
- Ratio ≈ 1.46 (rounded to two decimal places)
3. Interpret the ratio:
- The ratio indicates that, theoretically, HCl effuses approximately 1.46 times faster than NH3.
Therefore, based on the given relationship, the theoretical effusion rate of HCl is approximately 1.46 times faster than the theoretical effusion rate of NH3.