A balloon contains 0.113 mol of gas and has a volume of 3.06 L. 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 after adding 0.178 mol of gas, we can use the principle of Avogadro's Law, which states that equal volumes of gases at the same temperature and pressure contain equal numbers of moles.
Initially, the balloon contains 0.113 mol of gas and has a volume of 3.06 L.
After adding 0.178 mol of gas, the total number of moles of gas in the balloon is now 0.113 mol + 0.178 mol = 0.291 mol.
Since the total number of moles of gas has increased, the final volume of the balloon can be calculated using the equation:
V1 / n1 = V2 / n2
where:
V1 = initial volume = 3.06 L
n1 = initial moles = 0.113 mol
n2 = final moles = 0.291 mol
V2 = final volume
Plugging the values into the equation:
3.06 L / 0.113 mol = V2 / 0.291 mol
V2 = (3.06 L * 0.291 mol) / 0.113 mol
V2 = 7.857 L
Therefore, the final volume of the balloon after adding 0.178 mol of gas is 7.857 L, rounded to three significant figures.