I am stuck on this now....As a birthday balloon is filled with helium, the amount of helium increases from 0.5 moles of helium to 5.5 moles of helium. If the initial volume of the balloon is 2.5 mL, what is the final volume?
P V = n R T
T is constant
assume P is pretty constant, room pressure. Inside balloon is not much higher than outside because material is very weak.
V = (R T/P) n where (RT/P) is constant
so V2 / n2 = V1 / n1
V2/ 5.5 = 2.5 / 0.5
V2 = 2 (2.5 * 5.5) mL
so what is 5 * 5.5 :) ?
To solve this problem, we can use the ideal gas law equation, which states:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Ideal gas constant (0.0821 L•atm/(mol•K))
T = Temperature (assumed constant)
In this case, the pressure and temperature aren't given, but since the question asks about the change in volume, we can assume T and P remain constant.
Let's use the initial conditions to find the initial volume:
V1 = (n1 * R * T) / P
Given:
n1 = 0.5 moles
V1 = 2.5 mL (we will convert it to liters later)
R = 0.0821 L•atm/(mol•K)
Assuming T and P remain constant, we can simplify the equation to:
V1 = (0.5 * 0.0821 * T) / P
Next, we need to find the final volume (V2) when there are 5.5 moles of helium:
V2 = (n2 * R * T) / P
Given:
n2 = 5.5 moles
Assuming T and P remain constant, we can simplify the equation to:
V2 = (5.5 * 0.0821 * T) / P
Since T and P are assumed to be constant, their values do not change. We can simplify the equations further:
V1 = 0.04105 / P
V2 = 0.45355 / P
To find the ratio of V2 to V1, we can divide V2 by V1:
(V2 / V1) = (0.45355 / P) / (0.04105 / P)
= 0.45355 / 0.04105
= 11
Therefore, the final volume (V2) is 11 times the initial volume (V1).
To find the final volume, we multiply the initial volume by the ratio:
Final Volume = V1 * (V2 / V1)
= 2.5 mL * 11
= 27.5 mL
Therefore, the final volume of the balloon is 27.5 mL.
To find the final volume of the balloon, we can use the concept of Boyle's Law, which states that the product of the initial volume and pressure is equal to the product of the final volume and pressure.
Boyle's Law can be written as:
P1V1 = P2V2
Where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
In this case, the initial volume is given as 2.5 mL (or 0.0025 L), and we need to find the final volume.
We are also given the initial and final amount of moles of helium. Since the amount of the gas (n) is directly proportional to the volume (V) when pressure and temperature are constant, we can assume that the final amount of helium (n2) is directly proportional to the final volume (V2).
n1/V1 = n2/V2
Substituting the given values, we have:
(0.5 moles) / (0.0025 L) = (5.5 moles) / (V2)
To solve for V2, we can cross-multiply:
0.5 moles x V2 = 0.0025 L x 5.5 moles
0.5 x V2 = 0.01375
Dividing both sides by 0.5, we get:
V2 = 0.01375 / 0.5
V2 = 0.0275 L
Therefore, the final volume of the balloon is 0.0275 L (or 27.5 mL).