What is the relationship between the density of a gas and its molar mass at constant temperature and pressure?

1 question

1 item

Q: What is the relationship between the density of a gas and its molar mass at constant temperature and pressure?

Solution: At constant temperature and pressure, density is directly proportional to molar mass according to the ideal gas law.

Steps: 6

Step 1: Understand that density is the mass of a substance divided by its volume (Density = Mass/Volume).
Step 2: Recall the ideal gas law, which states that PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.
Step 3: Recognize that the number of moles (n) can be expressed as mass (m) divided by molar mass (M), so n = m/M.
Step 4: Substitute n in the ideal gas law: PV = (m/M)RT.
Step 5: Rearrange the equation to find density (ρ = m/V): ρ = PM/(RT).
Step 6: Notice that at constant temperature (T) and pressure (P), the density (ρ) is directly proportional to the molar mass (M).