Manipulating the PV=nRT Equation for Helium Balloon Volume

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In summary, the problem involves a balloon with an initial volume of 20 grams of helium at a pressure of 1000 torr. After releasing some of the helium, the new pressure is 900 torr and the volume is halved. The task is to determine the amount of helium in the balloon after the change, assuming the temperature remains constant. Using the ideal gas law, the amount of helium is calculated to be approximately 9 grams. However, the notation and explanation could be improved to better show the initial and final states and their corresponding values.
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brake4country
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Homework Statement


A balloon initially contains 20 grams of helium at a pressure of 1000 torr. After some helium is let out of the balloon the new pressure is 900 torr, and the volume is half of what it was. If the temperature has not changed, how much helium is now in the balloon?

Homework Equations


PV=nRT

The Attempt at a Solution


I first converted the grams to moles and the pressure to atm. I attempted this problem by setting the first and after values to each other. I used PV/n = PV/n (before and after). When I set these equal to each other I get approx. 4.6 mol He or approx. 9 grams He. Is this a legal way to approach this problem?
 
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brake4country said:
legal way
Conditionally. The notation is not what it could be. Subscripts, insertion of masses in the appropriate places would improve things.
brake4country said:
PV/n = PV/n (before and after)
It's not obvious that you've done anything without some remarks about initial and final "states" and values.
brake4country said:
approx. 9 grams He
Don't overuse the word "approximate" or its derivatives or abbreviations when you've got an exact answer based on the problem statement.
 

FAQ: Manipulating the PV=nRT Equation for Helium Balloon Volume

What is the Pv=nRT equation?

The Pv=nRT equation is also known as the ideal gas law, which describes the relationship between pressure (P), volume (V), amount of gas (n), temperature (T), and the gas constant (R) for an ideal gas. It is expressed as PV = nRT, where P is measured in atmospheres (atm), V in liters (L), n in moles (mol), T in Kelvin (K), and R is the universal gas constant with a value of 0.0821 L·atm/mol·K.

When is the Pv=nRT equation used?

The ideal gas law is used to calculate the properties of an ideal gas, which is a hypothetical gas that follows the assumptions of the kinetic theory of gases. It is commonly used in chemistry and physics to predict the behavior of gases at different temperatures, pressures, and volumes.

What are the assumptions of the Pv=nRT equation?

The ideal gas law assumes that the gas is in a state of thermodynamic equilibrium, the molecules of the gas are point particles with no volume or intermolecular forces, and the collisions between the gas molecules and the container walls are perfectly elastic. It also assumes that the gas particles are in constant random motion and that the average kinetic energy of the particles is directly proportional to the temperature of the gas.

Can the Pv=nRT equation be used for real gases?

The ideal gas law is an approximation and is most accurate for low pressures and high temperatures. Real gases deviate from ideal behavior at high pressures and low temperatures due to the presence of intermolecular forces and the finite volume of gas particles. However, the ideal gas law can still be used as a good estimate for real gases under certain conditions.

What are the units for the gas constant (R) in the Pv=nRT equation?

The units for the gas constant (R) in the ideal gas law are dependent on the units used for pressure, volume, amount of gas, and temperature. However, the most common units for R are liter·atm/mol·K. In SI units, the value of R is 8.314 J/mol·K.

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