To determine the density of argon gas at standard temperature and pressure (STP), follow these steps:
1. Identify Known Values:
- The molar mass of argon (Ar) is 39.948 grams per mole (g/mol).
- Standard temperature (STP) is 273.15 Kelvin (K), which is equal to 0 degrees Celsius.
- Standard pressure (STP) is 1 atmosphere (atm).
- The ideal gas constant (R) is 0.0821 L·atm/(mol·K).
2. Using the Ideal Gas Law:
The ideal gas law is given by:
[tex]\[ PV = nRT \][/tex]
Rearrange the equation to solve for the density (ρ), where the number of moles (n) is given by [tex]\( n = \frac{m}{M} \)[/tex] (m is the mass, M is the molar mass).
3. Derive the Density Formula:
From the ideal gas law, solve for density:
[tex]\[ \text{Density} = \frac{\text{Molar Mass} \times \text{Pressure}}{\text{R} \times \text{Temperature}} \][/tex]
Substitute the known values into the density formula:
[tex]\[ \text{Density of Argon} = \frac{39.948 \times 1}{0.0821 \times 273.15} \][/tex]
4. Calculate the Density:
[tex]\[ \text{Density of Argon} = \frac{39.948}{22.413415} \approx 1.7813558290374645 \text{ g/L} \][/tex]
5. Round to Three Significant Figures:
The density of argon is approximately [tex]\( 1.781 \)[/tex] g/L when rounded to three significant figures.
Therefore, the density of argon gas at STP is [tex]\( 1.781 \)[/tex] g/L.
