Solving Ideal Gas Question: Calculating Total Hydrogen and # of Balloons

In summary: This can be calculated by finding the volume of gas at the reduced pressure and subtracting it from the initial volume of gas in the cylinder. This will give you the total volume of gas used to fill the balloons. Then, you can divide this volume by the volume of gas in each balloon to find the number of balloons that can be filled. In summary, to find the number of balloons that can be filled from the cylinder, you need to find the total volume of gas used to fill the balloons by subtracting the volume at the reduced pressure from the initial volume, and then divide this by the volume of gas in each balloon.
  • #1
jiayingsim123
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0

Homework Statement


A gas cylinder contains 4.00 × 10^4cm^3 of hydrogen at a pressure of 2.50 × 10^7Pa and a
temperature of 290K.
The cylinder is to be used to fill balloons. Each balloon, when filled, contains
7.24 × 10^3cm^3 of hydrogen at a pressure of 1.85 × 10^5Pa and a temperature of 290 K.
Calculate, assuming that the hydrogen obeys the equation: PV = constant x T,
(i) the total amount of hydrogen in the cylinder,
(I've calculated this to be 415 moles, which is the right answer.)

(ii)the number of balloons that can be filled from the cylinder.



Homework Equations


P1V1=P2V2
PV=nRT

The Attempt at a Solution


The part I'm having problems with is b(ii). What I did was I divided the number of moles of the gas contained in the cylinder by the number of moles each balloon should contain when filled, but the answer I got is 746 whilst the correct answer is 741. The mark scheme says that I'm supposed to find out what the volume of the gas is at the reduced pressure of 1.85x10^5Pa and then subtract that volume by the volume of hydrogen in the gas to find out the total volume that is filled into the balloons. I don't see the rationale behind doing this so I'm hoping you guys can help me figure it out!

Thanks! :)
 
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  • #2
I think you should take into account that some gas will be left in the cylinder, which you can't use to fill balloons.
 

1. How do you calculate the total amount of hydrogen in an ideal gas?

To calculate the total amount of hydrogen in an ideal gas, you 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 in Kelvin. Rearrange this equation to solve for n, which represents the number of moles of hydrogen in the gas. Then, multiply the number of moles by the molar mass of hydrogen (2.016 g/mol) to get the total amount of hydrogen in grams.

2. How do you determine the number of balloons that can be filled with a certain amount of hydrogen?

To determine the number of balloons that can be filled with a certain amount of hydrogen, you can use the ideal gas law equation once again. This time, you will solve for V, which represents the volume of the gas. Divide the total amount of hydrogen (in moles) by the number of moles of hydrogen that can fill one balloon (this will vary depending on the size of the balloon). This will give you the total volume of the gas, and you can then divide this by the volume of one balloon to get the number of balloons that can be filled.

3. What is an ideal gas?

An ideal gas is a theoretical gas that follows the ideal gas law at all temperatures and pressures. This means that it has no intermolecular forces or volume, and its particles have no size. In reality, no gas is truly ideal, but some gases behave similarly to an ideal gas under certain conditions.

4. How does temperature affect the ideal gas law?

Temperature directly affects the ideal gas law through the variable T, which represents temperature in Kelvin. As temperature increases, the kinetic energy of the gas particles also increases, causing them to move faster and collide with the container walls more frequently. This results in an increase in pressure and volume, according to the ideal gas law equation.

5. Can the ideal gas law be used for all gases?

No, the ideal gas law can only be used for gases that behave similarly to an ideal gas. This includes gases that have low densities, high temperatures, and low pressures. Real gases deviate from ideal gas behavior at high pressures and low temperatures, so the ideal gas law cannot be applied to them accurately. Additionally, gases with strong intermolecular forces, such as water vapor, will not follow the ideal gas law.

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