Final answer:
To find the volume in liters of CO₂ produced, convert the given number of molecules to moles using Avogadro's number. Then use the ideal gas law equation V = nRT/P, substituting the values and calculate the volume in liters. The volume of CO₂ produced is approximately 31.9 L.
Step-by-step explanation:
To find the volume in liters of CO₂ produced, we need to convert the given number of molecules to moles using Avogadro's number. Then we can use the ideal gas law equation PV = nRT, where P is the pressure (assume it's constant), V is the volume in liters, n is the number of moles, R is the gas constant, and T is the temperature (assume it's constant as well). Rearranging the equation, V = nRT/P. Substitute the values for n, R, and P, and calculate the volume in liters.
Given:
- Number of molecules = 8.7 × 10²⁵
- Density of CO₂ = 1.98 kg/m³ = 1980 g/m³
- 1 L = 1 dm³
Step 1: Convert molecules to moles
n = 8.7 × 10²⁵ molecules / (6.022 × 10²³ molecules/mol) = 1.4452 mol
Step 2: Use the ideal gas law equation
V = nRT/P
Assume the temperature is constant at standard conditions (273 K) and the pressure is also constant at standard pressure (1 atm).
V = (1.4452 mol)(0.0821 L·atm/mol·K)(273 K) / (1 atm) = 31.944017 L ≈ 31.9 L
So, the volume of CO₂ produced is approximately 31.9 L.