Understanding the Concepts
* STP (Standard Temperature and Pressure): 0°C (273.15 K) and 1 atm pressure.
* Ideal Gas Law: PV = nRT, where:
* P = Pressure
* V = Volume
* n = Number of moles
* R = Ideal gas constant (0.0821 L·atm/mol·K)
* T = Temperature
* Density: Mass per unit volume (ρ = m/V)
Calculations
1. Molar Mass of CO2: The molar mass of CO2 is 44.01 g/mol (12.01 g/mol for carbon + 2 * 16.00 g/mol for oxygen).
2. Using the Ideal Gas Law: We can rearrange the Ideal Gas Law to solve for volume (V):
V = nRT/P
3. Substituting for n (moles): Since density is mass per volume, we can express the number of moles (n) as mass (m) divided by molar mass (M):
n = m/M
Substituting this into the volume equation:
V = (m/M)RT/P
4. Rearranging for Density: We can rearrange the volume equation to solve for density (ρ = m/V):
ρ = (m/V) = (PM)/(RT)
5. Plugging in Values: Now we plug in the values for CO2 at STP:
ρ = (1 atm * 44.01 g/mol) / (0.0821 L·atm/mol·K * 273.15 K)
6. Calculating the Density:
ρ ≈ 1.96 g/L
Therefore, the density of CO2 gas at STP is approximately 1.96 g/L.
