If an additional 0.178 mol of gas is added to the balloon (at constant temperature and pressure), what is its final volume?
Express your answer in liters to three significant figures.
To find the final volume of the balloon, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (constant)
V = volume
n = number of moles
R = ideal gas constant
T = temperature (constant)
Since the pressure and temperature are constant, we can simplify the equation to:
V1/n1 = V2/n2
Where:
V1 = initial volume
n1 = initial number of moles
V2 = final volume
n2 = final number of moles
Given:
V1 = 8.23 L
n1 = 0.377 mol
n2 = n1 + 0.178 mol = 0.555 mol
Now we can rearrange the equation to solve for V2:
V2 = V1 * (n2 / n1)
V2 = 8.23 L * (0.555 mol / 0.377 mol)
V2 = 12.09 L
Therefore, the final volume of the balloon is 12.09 liters.