Question

(a) How is the law of combining volumes explained by Avogadro's hypothesis? (b) Consider a 1.0-L flask containing neon gas and a 1.5-L flask containing xenon gas. Both gases are at the same pressure and temperature. According to Avogadro's law, what can be said about the ratio of the number of atoms in the two flasks?

Short answer

(a) Avogadro's hypothesis, which states that equal volumes of all gases at the same temperature and pressure have the same number of molecules, explains the law of combining volumes by showing that the whole number ratios in the volumes of reacting gases and gaseous products correspond to the small whole number ratios of their molecules. (b) For the given flasks containing neon and xenon gas at the same temperature and pressure, the ratio of the number of neon atoms to the number of xenon atoms is 2:3, determined by the ratio of their volumes (1.0 L / 1.5 L).

Step-by-step solution

Understanding Avogadro's Hypothesis and the Law of Combining Volumes

Avogadro's hypothesis states that equal volumes of all gases, at the same temperature and pressure, have the same number of molecules. The law of combining volumes states that the volumes of reacting gases, and the volumes of the gaseous products, are in small whole-number ratios when measured at the same temperature and pressure. To explain the law of combining volumes using Avogadro's hypothesis, we remember that the number of molecules in equal volumes of gases at the same temperature and pressure is the same, regardless of the gas type. Therefore, if two gases react in a specific volume ratio, the same number ratio applies for their molecules. This number ratio represents the small whole numbers mentioned in the law of combining volumes. Thus, Avogadro's hypothesis helps explain the law of combining volumes in terms of molecule numbers.

Finding the Ratio of Atoms in Two Flasks

In this case, we have a 1.0-L flask containing neon gas and a 1.5-L flask containing xenon gas. Both gases are at the same pressure and temperature. According to Avogadro's law, the number of atoms in these flasks can be compared. Since the volume of the neon gas flask is 1.0 L and the volume of the xenon gas flask is 1.5 L, we can set up the following ratio, using the relationship of Avogadro's hypothesis (the number of atoms is directly proportional to the volume of gas, for the same temperature and pressure): Ratio of atoms (Ne:Xe) = Volume ratio (Ne:xenon) = 1.0 L / 1.5 L

Calculating the Ratio of Atoms in Two Flasks

To calculate the ratio of atoms between the neon gas and xenon gas, we simply divide 1.0 L by 1.5 L: Ratio of atoms (Ne:Xe) = 1.0 L / 1.5 L = 2/3 So, according to Avogadro's law, the ratio of the number of neon atoms to the number of xenon atoms in the two flasks is 2:3.