Air is added to a balloon containing 10 moles of air. It increases in size from .2 M3 to .3 M3. How many moles are in the balloon now
To determine the number of moles added to the balloon, we need to calculate the change in volume and then use the ideal gas law.
Given:
Initial volume (V₁) = 0.2 m³
Final volume (V₂) = 0.3 m³
Initial number of moles (n₁) = 10
We can use the ideal gas law equation to find the number of moles in the final state:
PV = nRT
Assuming constant pressure and temperature, the equation can be simplified to:
V₁/n₁ = V₂/n₂
Rearranging the equation to find n₂:
n₂ = (V₂ * n₁) / V₁
Substituting the given values:
n₂ = (0.3 m³ * 10 mol) / 0.2 m³
n₂ = 3 * 10 mol
n₂ = 30 moles
Therefore, there are 30 moles in the balloon now.
To find the number of moles in the balloon after air is added, we can use the ideal gas law equation:
PV = nRT
where:
P = pressure of the gas
V = volume of the gas
n = number of moles of the gas
R = ideal gas constant
T = temperature of the gas
Since the pressure and temperature are assumed to be constant, we can simplify the equation to:
V1 / n1 = V2 / n2
where:
V1 = initial volume of the gas (0.2 m3)
n1 = initial number of moles of the gas (10 moles)
V2 = final volume of the gas (0.3 m3)
n2 = final number of moles of the gas (unknown)
Plugging in the values we know:
0.2 / 10 = 0.3 / n2
Simplifying the equation:
n2 = (0.3 * 10) / 0.2
n2 = 3 moles
Therefore, there are 3 moles of air in the balloon now.
To find how many moles are in the balloon after air is added, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure (which we assume to be constant),
V is the volume of the balloon,
n is the number of moles,
R is the ideal gas constant, and
T is the temperature (which we also assume to be constant).
We can rearrange the equation to solve for the number of moles:
n = PV / RT
Given:
Initial volume, V1 = 0.2 m^3
Final volume, V2 = 0.3 m^3
Initial number of moles, n1 = 10 moles
Assuming constant pressure and temperature, the equation becomes:
n2 = (V2 / V1) * n1
Plugging in the values:
n2 = (0.3 / 0.2) * 10
n2 = 1.5 * 10
n2 = 15 moles
Therefore, there are 15 moles of air in the balloon after air is added.