A party balloon filled with helium deflates to 2/3 of its original volume in 8.0 hours. How long will it take an identical balloon filled with the same number of moles of air (ℳ = 28.2 g/mol) to deflate to 1/2 of its original volume?
I know it's an effusion, so I did:
(2/3)/ (8 hrs) sqrt (28.2 g/mol)
_______________ = _____________
(1/2)/ (? hrs) sqrt (28.2 g/mol)
but I don't get the correct answer, which is 32 hours.
I think there's one other error in your substitution. Since the problem says 2/3 of He was left, where you have 2/3 in the substitution, you should have 1/3, since 1/3 was the amount effused.
2x/3*8=√28.2/√4.0
2X/24=2.655183609
x=31.86220331
x=32 hours
I think your only problem is that you didn't substitute correctly in the equation. The 28.2 you used twice. The one in the denominator should have been the one for He which will be 4. If I put 4 there I get 32.
Yes, that's correct! Good job catching the mistake in the substitution and solving it correctly. The correct answer is indeed 32 hours.
Well, it seems like you've been having some trouble with your balloon question. But don't worry, I'm here to lighten things up!
Why did the balloon go to therapy? Because it was feeling deflated!
Now, let's get back to your question. To solve this, we can 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 gas constant, and T is the temperature. Since the number of moles and gas constant are the same for both balloons, we can simplify the equation.
First, let's calculate how much the first balloon (with helium) deflates per hour. It deflates from 1 to 2/3 of its original volume in 8 hours. This means it deflates by 1/3 in 8 hours, so the deflation rate is 1/24 per hour.
Now, let's find out the deflation rate of the second balloon (with air). It deflates from 1 to 1/2 of its original volume in a certain number of hours. Let's call this unknown number of hours x. So, the deflation rate for the second balloon is 1/2 divided by x.
Since both deflation rates should be equal, we can set up an equation:
1/24 = 1/2x
To solve this equation, we can cross-multiply:
x = 2/24
Now, simplifying the right side of the equation gives:
x = 1/12
So, it would take the second balloon (with air) 1/12 hours to deflate to 1/2 of its original volume.
However, this answer doesn't match the correct answer of 32 hours that you mentioned. So, there might be an error in the given information or calculation. Double-check your numbers, and if you still need help, I'm here to assist you with more jokes and explanations!
To solve this problem, you're on the right track by using the concept of effusion and applying the principles of Boyle's Law. However, it looks like you made a mistake in your calculation. Let's break it down step by step:
First, let's define the variables:
V1 = Original volume of the first balloon (unknown)
V2 = Final volume of the first balloon (2/3 of V1)
t1 = Time taken for the first balloon to deflate (8.0 hours)
V3 = Original volume of the second balloon (unknown)
V4 = Final volume of the second balloon (1/2 of V3)
t2 = Time taken for the second balloon to deflate (unknown)
M = Molar mass of air = 28.2 g/mol
According to Boyle's Law, the ratio of initial and final volumes (V1/V2 or V3/V4) is equal to the ratio of the corresponding times taken to deflate (t1/t2) when the molar mass is kept constant.
Therefore, the equation becomes:
(V1/V2) = (t1/t2) * sqrt(M/M)
Plugging in the values we know:
(V1/[(2/3)V1]) = (8.0/t2) * sqrt(28.2/28.2)
Simplifying the equation:
(3/2) = (8.0/t2)
Cross-multiplying and solving for t2:
t2 = (8.0 * 2) / 3
t2 = 16.0 / 3
t2 ≈ 5.33 hours
So, according to the calculations, it should take the second balloon approximately 5.33 hours to deflate to 1/2 of its original volume, not 32 hours.
Therefore, it seems there was an error in the answer provided for the correct time.