A balloon contains 0.126mol of gas and has a volume of 2.78L.
If an additional 7.0×10−2mol of gas is added to the balloon, what will its final volume be?
n1 = 0.126
n2 = 0.126+0.07 = ?
(V1/n1) = (V2/n2)
Thank you. That helped a lot.
To solve this problem, we need to use the ideal gas law equation, which states:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
In this case, we are looking for the final volume (Vf) when an additional amount of gas is added to the balloon. We can assume that the pressure (P) and temperature (T) remain constant.
Step 1: Calculate the initial volume (Vi) of the balloon:
Given that the balloon initially contains 0.126 mol of gas and has a volume of 2.78 L, we can write:
Vi = 2.78 L
Step 2: Calculate the total number of moles (n_total) in the balloon after the additional gas is added:
To find the total number of moles, we add the initial moles (0.126 mol) to the moles added (7.0×10−2 mol):
n_total = 0.126 mol + 7.0×10−2 mol
n_total = 0.196 mol
Step 3: Use the combined volume of the moles to find the final volume (Vf):
We assume the pressure, temperature, and moles have all remained constant, so we can use the equation:
V_initial × n_initial = V_final × n_final
Plugging in the known values:
2.78 L × 0.126 mol = V_final × 0.196 mol
Rearranging the equation to solve for V_final:
V_final = (2.78 L × 0.126 mol) / 0.196 mol
Calculating the final volume:
V_final = 1.7928 L
Therefore, the final volume of the balloon will be approximately 1.7928 L when an additional 7.0×10−2mol of gas is added.