To determine the volume of the cylinder after the reaction, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (assumed constant)
V = volume
n = number of moles of gas
R = ideal gas constant
T = temperature (assumed constant)
Since the temperature and pressure are assumed to be constant, we can rewrite the equation as:
V1/n1 = V2/n2
Where:
V1 = initial volume
n1 = initial number of moles of gas
V2 = final volume
n2 = final number of moles of gas
Given:
V1 = 2.1 L (initial volume)
n1 = 0.11 mol (initial moles of gas)
n2 = 0.11 mol + 0.58 mol (initial moles of gas + moles produced in the reaction)
Calculating the final volume:
V1/n1 = V2/n2
2.1 L / 0.11 mol = V2 / (0.11 mol + 0.58 mol)
19.09 L/mol = V2 / 0.69 mol
V2 = 19.09 L/mol * 0.69 mol
V2 ≈ 13.17 L
Therefore, the volume of the cylinder after the reaction is approximately 13.17 L.