How many grams of helium must be added to a balloon containing 8.00 g of helium gas to double its volume. Assume no temp or pressure change.
the pressure and temp being constant, you would add 8.00g of helium to the 8.00g to double its volume. If pressure or temp were varied this would not be true.
Well, I have to say, balloons do have quite an inflated ego. But to solve this problem, we don't need any fancy tricks. If we want to double the volume of the balloon, we need to add an equal amount of helium gas. So, since we already have 8.00 grams of helium gas, we need to add another 8.00 grams to the balloon. Just make sure you don't let it go, or else it will really become a "weightless" situation!
To double the volume of a balloon, we need to calculate the additional amount of helium gas required. Let's assume the initial volume of the balloon is V grams.
Since the gas law states that the volume of a gas is directly proportional to the amount of gas, we can set up a proportion:
Initial volume of helium gas / Initial amount of helium gas = Final volume of helium gas / Final amount of helium gas
Let's represent the initial amount of helium gas as N1 (8.00 g) and the final volume of helium gas as V2 (2V, as we want to double the volume).
N1 / V = N2 / 2V
Cross multiplying, we get:
2V * N1 = N2 * V
Simplifying further:
2N1 = N2
So, the final amount of helium gas required (N2) will be twice the initial amount (N1).
N2 = 2 * N1
= 2 * 8.00 g
= 16.00 g
Therefore, you would need to add 16.00 grams of helium gas to the balloon to double its volume.
To determine the amount of helium that needs to be added to double the volume of the balloon, we need to use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature (which is assumed to be constant in this case).
Since the question states that there is no temperature or pressure change, we can assume that both will remain constant. Therefore, our equation simplifies to:
V1 / n1 = V2 / n2
Let's assign variables to the given values:
V1 = initial volume
n1 = initial number of moles (corresponding to the initial mass of helium)
V2 = final volume (double the initial volume)
n2 = unknown (representing the additional moles needed)
From the information given, we have:
V1 = V2 / 2
n1 = 8.00 g (initial mass of helium)
Now, we need to convert the mass of helium into moles. To do this, we use the molar mass of helium, which is 4 g/mol:
n1 = (8.00 g) / (4 g/mol) = 2.00 mol
Now, let's substitute the values into our equation:
V1 / n1 = V2 / n2
(V2 / 2) / 2.00 = V2 / n2
Simplifying the equation, we get:
1 / 2 = 1 / n2
To solve for n2, we invert both sides of the equation:
2 / 1 = n2 / 1
n2 = 2 moles
Since the molar mass of helium is 4 g/mol, we can calculate the additional mass of helium needed to add, using the number of moles:
Mass = (n2) * (molar mass of helium)
Mass = (2 mol) * (4 g/mol) = 8.00 g
Therefore, to double the volume of the balloon, you would need to add an additional 8.00 grams of helium gas.