To find the mass of carbon dioxide (CO₂) under given conditions, we will use the Ideal Gas Law, which is expressed as:
PV = nRT
Where:
- P = Pressure in atmospheres (atm)
- V = Volume in liters (L)
- n = Number of moles of gas
- R = Ideal gas constant (0.0821 L·atm/(K·mol))
- T = Temperature in Kelvin (K)
Step 1: Convert Units
- Pressure Conversion:
- 20 psi to atm:
\( P = 20 \, \text{psi} \times \frac{1 \, \text{atm}}{14.696 \, \text{psi}} \approx 1.36 \, \text{atm} \)
- Volume Conversion:
- 10 ft³ to liters:
\( V = 10 \, \text{ft}^3 \times 28.3168 \, \text{L/ft}^3 \approx 283.168 \, \text{L} \)
- Temperature Conversion:
- 200°F to Kelvin:
\( T = \frac{200 - 32}{1.8} + 273.15 \approx 366.48 \, \text{K} \)
Step 2: Calculate Moles of CO₂
Using the Ideal Gas Law:
- Rearranging for n:
\( n = \frac{PV}{RT} \)
Plugging in the values:
- \( n = \frac{(1.36 \, \text{atm})(283.168 \, \text{L})}{(0.0821 \, \text{L·atm/(K·mol)})(366.48 \, \text{K})} \approx 13.52 \, \text{mol} \)
Step 3: Calculate Mass of CO₂
- Molar mass of CO₂ = 44.01 g/mol.
- Mass calculation:
\( \text{Mass} = n \times \text{Molar Mass} \)
\( \text{Mass} = 13.52 \, \text{mol} \times 44.01 \, \text{g/mol} \approx 595.3 \, \text{g} \)
Final Result
- The mass of carbon dioxide is approximately 595.3 grams.