# Calculate Mass of Balloon with PV=mRT

• GoSS190
In summary, the ideal gas law equation (PV=mRT) can be used to calculate the mass of a balloon by relating its pressure, volume, temperature, and mass. It is an important tool in many scientific and engineering applications, but it has limitations such as assuming ideal gas behavior and being most accurate under certain conditions. Knowing the mass of a balloon is important for determining its buoyancy and flight characteristics, as well as for safety and engineering considerations. The units of measurement used in the ideal gas law equation are pressure (in atm), volume (in liters), mass (in grams), the ideal gas constant (in L*atm/mol*K), and temperature (in Kelvin).
GoSS190

## Homework Statement

A balloon contains 6000m^3 of helium at 28 degrees C. and 99kPa absolute. Just before launch determine the mass of the balloon.

## Homework Equations

Determine the mass of the balloon.

## The Attempt at a Solution

I think you might have to use PV=mRT but I am not sure about how you would get R really. Any thoughts? Is that the right equation to use here?

R = 8.314 / Molecular Weight of helium

Yes, you are correct, the ideal gas law, PV=mRT, is the appropriate equation to use in this situation. R is the universal gas constant, which is a constant value that is typically given to you in the problem or can be looked up. In this case, it is 8.314 J/mol*K.

To solve for the mass of the balloon, you will need to rearrange the equation to solve for m, the mass. This would give you m=PV/RT. Plug in the given values for P, V, T, and R, and you will get the mass of the balloon in kilograms.

It is important to note that this equation assumes the gas inside the balloon is behaving like an ideal gas, which may not always be the case. However, for most gases at moderate temperatures and pressures, this equation provides a reasonable estimate.

## 1. How do you calculate the mass of a balloon using the ideal gas law equation PV=mRT?

The mass of a balloon can be calculated using the following equation:m = (PV)/(RT)Where:P is the pressure of the gas inside the balloonV is the volume of the balloonm is the mass of the gasR is the ideal gas constant (0.0821 L*atm/mol*K)T is the temperature of the gas in Kelvin

## 2. What is the ideal gas law equation used for?

The ideal gas law equation (PV=mRT) is used to relate the physical properties of a gas (pressure, volume, temperature, and mass) to each other. It is based on the ideal gas law, which assumes that the gas particles are in constant motion and have no volume or intermolecular forces, making it a useful tool for calculating gas properties in many scientific and engineering applications.

## 3. Why is it important to know the mass of a balloon?

The mass of a balloon is important because it affects its buoyancy and flight characteristics. Knowing the mass can also help in determining the amount of gas needed to inflate the balloon to a desired size and lift capacity. Additionally, the mass of the balloon can provide important information for safety and engineering considerations in applications such as hot air balloons or weather balloons.

## 4. What are the units of measurement used in the ideal gas law equation?

The units of measurement in the ideal gas law equation (PV=mRT) are:P - pressure (in atm)V - volume (in liters)m - mass (in grams)R - ideal gas constant (in L*atm/mol*K)T - temperature (in Kelvin)

## 5. What are some limitations of using the ideal gas law to calculate the mass of a balloon?

There are a few limitations to using the ideal gas law equation to calculate the mass of a balloon. The ideal gas law assumes that the gas particles have no volume and no intermolecular forces, which is not always the case in real-world scenarios. Additionally, the ideal gas law is most accurate at low pressures and high temperatures, so it may not be as accurate for gases under extreme conditions. Other factors such as the material and thickness of the balloon, as well as external factors like wind and temperature gradients, can also affect the accuracy of the calculated mass.

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