Suppose you have two 1-L flasks, one containing N2 at STP, the other containing CH4 at STP. How do these systems compare with respect to (a) number of molecules?

Verified step by step guidance

1. Identify that STP (Standard Temperature and Pressure) conditions imply that both gases are at 0°C (273.15 K) and 1 atm pressure.
2. Recall that at STP, one mole of any ideal gas occupies 22.4 L. Since each flask has a volume of 1 L, calculate the number of moles of gas in each flask by using the formula: Moles = Volume / 22.4 L.
3. Use Avogadro's Law, which states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. This implies that the number of moles (and thus the number of molecules) in each flask should be the same under these conditions.
4. Calculate the number of molecules in each flask by multiplying the number of moles by Avogadro's number (approximately 6.022 x 10^23 molecules/mole).
5. Conclude that the number of molecules in the flask containing N2 is equal to the number of molecules in the flask containing CH4 under the given conditions.

Key Concepts

Avogadro's Law

Avogadro's Law states that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules. This principle is crucial for comparing the number of molecules in the two flasks since both are at standard temperature and pressure (STP), allowing us to directly relate their volumes to the number of molecules present.

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) is defined as a temperature of 0 degrees Celsius (273.15 K) and a pressure of 1 atmosphere. At STP, one mole of any ideal gas occupies a volume of 22.4 liters. This concept is essential for determining the number of moles and, consequently, the number of molecules in the gas samples contained in the flasks.

Molar Volume of a Gas

The molar volume of a gas is the volume occupied by one mole of a gas at STP, which is 22.4 liters. Since both flasks contain 1 liter of gas, we can calculate the number of moles in each flask by dividing the volume by the molar volume. This allows us to determine the number of molecules in each gas sample using Avogadro's number.