How many moles of gas are in the balloon?

In summary, the conversation discusses the calculation of the number of moles and oxygen molecules present in a spherical balloon inflated to a diameter of 36 cm. The correct formula to use is PV = nRT, where the temperature must be in Kelvin and the pressure in Pascals. The correct answer for the number of moles is 1.02, and the volume of the gas must be calculated correctly.
  • #1
roam
1,271
12

Homework Statement



A spherical balloon is inflated to a diameter of 36 cm. Assuming that the gas in the balloon is of atmospheric pressure (101.3 kPa) and is at a temperature of 20°C.

(a) How many moles of gas are in the balloon?

(b) If 21% of the molecules in the balloon are oxygen molecules, how many oxygen molecules are in the balloon?

The Attempt at a Solution



(a) I want to use the formula [tex]PV=nRT[/tex]

Volume is [tex]v=\frac{4}{3} \pi (0.18)^2 = 0.1357[/tex]

R is the constant 8.314

So [tex](101.3)(0.1357)=n8.314(20)[/tex]

Now if I solve for n I get [tex]n= {13.74}{166.28} = 0.082[/tex]

This is wrong because the correct answer must be 1.02. Do I need to convert the temprature to Kelvin/absolute temprature? ...because I tried that too & it didn't work.
 
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  • #2
Given pressure is in kilopascal.
Temperature must be in Kelvin.
 
Last edited:
  • #3
Temperature should be in kelvin
 
  • #4
Your temperature should be in Kelvin (K) and the pressure in Pa
 
  • #5
Also, you squared your radii instead of cubing it.
 
  • #6
Okay 20 degrees is 293.15 in Kelvin, and I converted the pressure to pascals. So my equation becomes

[tex](101300)(0.1357)=n(8.314)(293.15)[/tex]

n= 5.64

But why is this still not the right answer? :confused:
 
  • #7
roam said:
Okay 20 degrees is 293.15 in Kelvin, and I converted the pressure to pascals. So my equation becomes

[tex](101300)(0.1357)=n(8.314)(293.15)[/tex]

n= 5.64

But why is this still not the right answer? :confused:
Check the volume of the gas.
V = 4/3*π*r^3
 
  • #8
= [. I said that earlier. I'm sad now.
 

1. How do you calculate the number of moles of gas in a balloon?

To calculate the number of moles of gas in a balloon, you need to know the volume of the balloon, the temperature of the gas, and the pressure of the gas. Then, you can use the ideal gas law equation (PV = nRT) to solve for the number of moles (n).

2. What is the ideal gas law equation?

The ideal gas law equation is PV = nRT. P represents pressure (in atmospheres), V represents volume (in liters), n represents the number of moles, R is the universal gas constant (0.0821 L.atm/mol.K), and T represents temperature (in Kelvin).

3. Can the number of moles of gas in a balloon change?

Yes, the number of moles of gas in a balloon can change. It can change if the volume of the balloon changes, if the temperature of the gas changes, or if the pressure of the gas changes.

4. How does the number of moles of gas in a balloon affect its behavior?

The number of moles of gas in a balloon affects its behavior because it determines the amount of gas particles present. A larger number of moles means a larger number of gas particles, which can result in a larger volume and higher pressure inside the balloon.

5. How is the number of moles of gas related to the mass of the gas?

The number of moles of gas is directly proportional to the mass of the gas. This means that as the number of moles increases, so does the mass of the gas. The proportionality constant is the molar mass of the gas, which can be used to convert between moles and grams.

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