Atmospheric pressure/Gas laws

[woox]

Homework Statement

A balloon whose volume is 500 m^3 is to be filled with hydrogen at atmospheric pressure (1.01x10^5 Pa).
a. If the hydrogen is stored in cylinders of volume 2.5 m^3 at an absolute pressure of 35x10^5 Pa, how many cylinders are required? Assume temperature of hydrogen remains constant.
b.) What is the weight (in addition to weight of the gas) that can be supported by the balloon if the gas in the balloon and surrounding air are both at 0 degree C? The molecular mass of H2 is 2.02 g/mole. The density of air at 0 degree C and atmospheric pressure is 1.29 kg/m^3

c.( What weight could be supported If the balloon were filled with helium (with an atomic mass of 4 g/mole) instead of hydrogen, again at 0 degree C.

Homework Equations

PV=nRT?
V1T1=VfT2?

The Attempt at a Solution

I know I don't have any actual WORK for this problem, but that's because I have absolutely NO CLUE where to start. If anyone who is good at this kind of stuff, any help is appreciated. Thanks.

 

[Andrew Mason]

Homework Statement

A balloon whose volume is 500 m^3 is to be filled with hydrogen at atmospheric pressure (1.01x10^5 Pa).
a. If the hydrogen is stored in cylinders of volume 2.5 m^3 at an absolute pressure of 35x10^5 Pa, how many cylinders are required? Assume temperature of hydrogen remains constant.

What is the number of moles of hydrogen (H₂) needed? I think you are supposed to assume a temperature of 0 degrees C (273 K). That should give you a start.

AM

 

[m2003]

I can help guide you through solving this problem. First, let's start with the basics. Atmospheric pressure is the force per unit area exerted by the weight of the air above a given point in the atmosphere. It is measured in units of pressure such as Pascals (Pa) or millibars (mb). The gas laws, specifically Boyle's Law and Gay-Lussac's Law, describe the relationship between the volume, pressure, and temperature of a gas.

To solve this problem, we will use the Ideal Gas Law, which is PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant (8.31 J/mol·K), and T is temperature in Kelvin.

a. To find the number of cylinders required to fill the balloon, we need to use the Ideal Gas Law to solve for n, the number of moles of hydrogen. We know the volume of the balloon (500 m^3), the pressure of the hydrogen in the cylinders (35x10^5 Pa), and the temperature (which we will assume is constant). We also know that the volume of each cylinder is 2.5 m^3. Using the Ideal Gas Law, we can solve for n:

n = (PV)/(RT)

n = [(35x10^5 Pa)(500 m^3)]/[(8.31 J/mol·K)(273 K)]

n = 80,000 moles of hydrogen

Since each cylinder contains 2.5 m^3 of hydrogen, we will need 80,000 moles/2.5 m^3 = 32,000 cylinders to fill the balloon.

b. To find the weight that can be supported by the balloon, we need to consider the weight of the gas in the balloon and the weight of the surrounding air. We can calculate the weight of the gas in the balloon by using the Ideal Gas Law again:

n = (PV)/(RT)

n = [(1.01x10^5 Pa)(500 m^3)]/[(8.31 J/mol·K)(273 K)]

n = 23,000 moles of hydrogen

The weight of the gas in the balloon is then:

W = (n)(M)(g)

W = (23,000 moles)(2.02 g/mol)(9.8 m/s^2)

W =