How many atoms of He can a balloon that has a 21 cm diameter hold? The density of Helium is 1.18 g/L.
(Assume the balloon is a sphere).
v = 4/3 * π * d^3 / 8
calculate the volume , it will be in cm^3
... 1000 cm^3 = 1 L
find the mass of He in the balloon
... divide by the molar mass of He to find the moles of He
multiply the moles by Avogadro's number to find the number of atoms
Well, if the balloon is a sphere, then we can calculate its volume using the formula V = (4/3)πr^3, where r is the radius of the balloon.
Given that the diameter of the balloon is 21 cm, the radius would be half of that, which is 10.5 cm or 0.105 m.
So, the volume of the balloon would be V = (4/3)π(0.105)^3 = 0.005534 m^3.
Now, to calculate the number of atoms of helium the balloon can hold, we need to know the molar mass of helium. The molar mass of He is approximately 4 g/mol.
Given that the density of helium is 1.18 g/L, we can convert it to kg/m^3 by dividing by 1000: 1.18 g/L = 0.00118 kg/m^3.
Now, we can calculate the number of moles of helium using the formula: moles = mass/molar mass. The mass is equal to density times volume: mass = density x volume.
So, the mass of helium in the balloon is 0.00118 kg/m^3 x 0.005534 m^3 = 0.0000065 kg.
Now, we can calculate the number of moles: moles = 0.0000065 kg / 4 g/mol = 0.000001625 mol.
Since 1 mol contains approximately 6.02 x 10^23 atoms, we can find the number of atoms in the balloon by multiplying the number of moles by Avogadro's number.
Therefore, the balloon can hold approximately 9.79 x 10^16 atoms of helium. That's a whole lot of atoms! Hope this answer floats your boat... or balloon!
To find the number of atoms of Helium a balloon can hold, we need to follow these steps:
Step 1: Calculate the volume of the balloon.
The volume of a sphere can be calculated using the formula:
V = (4/3) * π * r^3
Given that the diameter of the balloon is 21 cm, the radius (r) can be calculated as half of the diameter: r = 21 cm / 2 = 10.5 cm = 0.105 m
Plugging this value into the volume formula:
V = (4/3) * π * (0.105 m)^3
Step 2: Convert the density of helium to the number of atoms per liter.
Given that the density of helium is 1.18 g/L, we need to convert this to the number of helium atoms per liter.
The molar mass of helium (He) is approximately 4 g/mol. This means that 1 mole of helium contains 6.022 x 10^23 atoms.
To calculate the number of helium atoms per liter, we divide the density by the molar mass and multiply by Avogadro's number:
Number of helium atoms per liter = (1.18 g/L / 4 g/mol) * (6.022 x 10^23 atoms/mol)
Step 3: Calculate the number of helium atoms in the balloon.
Now we can determine the number of helium atoms in the balloon by multiplying the volume of the balloon (in liters) by the number of helium atoms per liter.
Number of helium atoms = V * Number of helium atoms per liter
Let's calculate it step by step:
Step 1: Calculate the volume of the balloon.
V = (4/3) * π * (0.105 m)^3
Step 2: Convert the density of helium to the number of atoms per liter.
Number of helium atoms per liter = (1.18 g/L / 4 g/mol) * (6.022 x 10^23 atoms/mol)
Step 3: Calculate the number of helium atoms in the balloon.
Number of helium atoms = V * Number of helium atoms per liter
To calculate the number of helium atoms a balloon can hold, we need to follow these steps:
1. Determine the volume of the balloon: Since the balloon is assumed to be a sphere, we can find its volume using the formula for the volume of a sphere, V = (4/3) * π * r^3. Here, r represents the radius of the balloon, which is half of its diameter. The diameter of the balloon is given as 21 cm, so the radius would be 21 cm / 2 = 10.5 cm = 0.105 m.
Substituting the radius into the volume formula, we get V = (4/3) * π * (0.105 m)^3.
2. Convert the volume into liters: The density of helium is given as 1.18 g/L. To compare the volume of the balloon (in cubic meters) to the density (in grams per liter), we need to convert the volume from cubic meters to liters. Since 1 m^3 = 1000 L, we can convert the volume by multiplying it by 1000.
Converting the volume to liters, we have V = (4/3) * π * (0.105 m)^3 * 1000 L.
3. Calculate the mass of helium in the balloon: To find the mass, we can use the formula density = mass / volume. Rearranging this formula, mass = density * volume. Here, the density is 1.18 g/L (given), and the volume is the one we calculated in step 2.
Substituting the values, we get mass = 1.18 g/L * [(4/3) * π * (0.105 m)^3 * 1000 L].
4. Convert the mass into moles: To convert the mass of helium into moles, we need to use the molar mass of helium. The molar mass of helium is approximately 4 g/mol.
Calculating the moles of helium, we have moles = mass / molar mass. Substituting the mass and molar mass, we get moles = [(1.18 g/L * (4/3) * π * (0.105 m)^3 * 1000 L)] / 4 g/mol.
5. Calculate the number of atoms of helium: Once we have the moles of helium, we can use Avogadro's number, which is approximately 6.022 x 10^23 atoms/mol, to find the number of atoms.
Number of atoms = moles * Avogadro's number.
By following these steps, we can determine the number of helium atoms a balloon with a 21 cm diameter can hold.