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 (b) density?

Verified step by step guidance

1. Identify the molar masses of the gases. The molar mass of nitrogen (N2) is approximately 28 g/mol, and the molar mass of methane (CH4) is approximately 16 g/mol.
2. Recall that at STP (Standard Temperature and Pressure), one mole of any gas occupies 22.4 L. Since each flask contains 1 L of gas, calculate the number of moles of each gas in their respective flasks using the formula: number of moles = volume / 22.4 L.
3. Calculate the mass of each gas in the flasks by multiplying the number of moles by the molar mass of each gas. Use the formula: mass = number of moles × molar mass.
4. Determine the density of each gas using the formula: density = mass / volume. Since the volume of each flask is 1 L, the density can be directly calculated from the mass obtained in the previous step.
5. Compare the densities calculated for N2 and CH4 to determine which gas has a higher density under the same conditions.

Key Concepts

Density

Density is defined as mass per unit volume, typically expressed in grams per liter (g/L) for gases. It is an important property that helps compare different substances under the same conditions. For gases, density can be influenced by temperature and pressure, but at standard temperature and pressure (STP), it can be calculated using the ideal gas law.

Ideal Gas Law

The ideal gas law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law allows for the calculation of various properties of gases, including density.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is crucial for determining the density of gases, as density can be calculated using the formula: density = (molar mass) / (molar volume). At STP, one mole of any ideal gas occupies 22.4 liters, which allows for straightforward comparisons of densities based on their molar masses.