Question

If 8.7 × 10²⁵ molecules of CO₂ are produced in a combustion reaction, what is the volume in liters of CO₂ produced? (The density of CO₂ is 1.98 kg/m³, and 1 L = 1 dm³).

a. 4.39 L
b. 8.7 L
c. 17.4 L
d. 43.9 L

Answer 1

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.