A clown at a birthday party has brought along a helium cylinder, with which he intends to fill balloons. When full, each balloon contains 0.00410 m3 of helium at an absolute pressure of 1.30 x 105 Pa. The cylinder contains helium at an absolute pressure of 2.40 x 107 Pa and has a volume of 0.00260 m3. The temperature of the helium in the tank and in the balloons is the same and remains constant. What is the maximum number of people who will get a balloon?

Check my working please don't know where I got wrong..,

#Figure out moles in cylinder:
PV=nRT, solve for n,
(2.40x10^7)*(0.00260)/(8.31)(T is nothing, cause it remains constant)
= 7509 moles in cylinder

#FIgure moles in each balloon:
nballoon = (.0041)*(1.3x10^5)/(8.31)(T is nothing cause it remains constant)
= 64.14

#Number of people = 7509/64 = 117 people, this answer is wrong...check and tell me where I went wrong and how to fix it please :)

You made a mistake in your calculation for the number of moles in each balloon. You used the pressure of the helium in the cylinder instead of the pressure of the helium in the balloons. The pressure of the helium in the balloons is 1.30 x 105 Pa, not 2.40 x 107 Pa.

#Figure moles in each balloon:
nballoon = (.0041)*(1.3x10^5)/(8.31)(T is nothing cause it remains constant)
= 5.14

#Number of people = 7509/5.14 = 1463 people

To find the maximum number of people who will get a balloon, we need to determine the limiting reactant, which in this case is helium. We will compare the number of moles of helium in the cylinder with the number of moles required to fill each balloon.

First, let's calculate the number of moles of helium in the cylinder:
Using the ideal gas law (PV = nRT), we can rearrange the equation to solve for n (moles):
n = PV / RT

Given:
P (pressure in the cylinder) = 2.40 x 10^7 Pa
V (volume of the cylinder) = 0.00260 m^3
R (ideal gas constant) = 8.31 J/(mol·K)
T (temperature) remains constant.

n(cylinder) = (2.40 x 10^7 Pa) * (0.00260 m^3) / (8.31 J/(mol·K) * T)

Since the temperature is constant and not given, we can ignore the T term for now.

n(cylinder) = (2.40 x 10^7 Pa) * (0.00260 m^3) / (8.31 J/(mol·K))
n(cylinder) = 7509 moles of helium in the cylinder (approximately)

Next, let's calculate the number of moles of helium required to fill each balloon:
Using the ideal gas law again:

Given:
P (pressure in the balloon) = 1.30 x 10^5 Pa
V (volume of the balloon) = 0.00410 m^3
R (ideal gas constant) = 8.31 J/(mol·K)
T (temperature) remains constant.

n(balloon) = (1.30 x 10^5 Pa) * (0.00410 m^3) / (8.31 J/(mol·K) * T)
n(balloon) = 64.14 moles of helium per balloon (approximately)

Now, to find the maximum number of people who will get a balloon, divide the number of moles in the cylinder by the number of moles required for each balloon:

Number of people = n(cylinder) / n(balloon)
Number of people = 7509 moles / 64.14 moles
Number of people = 117.03

Therefore, the maximum number of people who will get a balloon is approximately 117.

To find the maximum number of people who will get a balloon, we need to consider the amount of helium available in the cylinder and the amount required to fill each balloon.

First, let's calculate the number of moles of helium in the cylinder.

Using the ideal gas law equation, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant (8.31 J/(mol·K)), and T is the temperature (which remains constant).

We can rearrange the equation to solve for n:

n = PV / RT

Plugging in the values given:
P_cylinder = 2.40 x 10^7 Pa
V_cylinder = 0.00260 m^3

n_cylinder = (P_cylinder * V_cylinder) / (R * T)

But since the temperature is constant and cancels out, we can ignore it for this calculation.

n_cylinder = (2.40 x 10^7 Pa * 0.00260 m^3) / (8.31 J/(mol·K))

n_cylinder ≈ 7319 moles

Next, let's calculate the number of moles of helium in each balloon.

Using the same ideal gas law equation, we can substitute the values given:
V_balloon = 0.00410 m^3
P_balloon = 1.30 x 10^5 Pa

n_balloon = (P_balloon * V_balloon) / (R * T)

Again, since the temperature remains constant, it cancels out in this calculation.

n_balloon = (1.30 x 10^5 Pa * 0.00410 m^3) / (8.31 J/(mol·K))

n_balloon ≈ 64.14 moles

Now, to find the maximum number of people who will get a balloon, we need to divide the number of moles in the cylinder by the number of moles in each balloon:

Maximum number of people = n_cylinder / n_balloon

Maximum number of people ≈ 7319 moles / 64.14 moles

Maximum number of people ≈ 114 people

Therefore, the correct answer is that a maximum of 114 people will be able to get a balloon.