Question

Help please?

You are going to complete several meteorological tests using a large weather balloon. You wish to check the temperature at 3000 meters altitude. You want to make sure the balloon will not burst before it reaches that height. Some calculations are needed. The balloon manufacturer guarantees the balloon up to 47.0 Liters in size.

Will the balloon make it to the necessary height without bursting? The temperature at ground level is 20 C. The pressure is 765 mmHg. The volume of the balloon prior to release is 30.0 Liters. It is filled with helium, which is lighter than air. For both calculations you will be using PV =nRT. Show all work for any credit.

1. Calculate the amount in grams of helium in the balloon. Hint remember n = moles

2. Can the balloon ascend to 3000 meters without bursting? The temperature and pressure at 3000 meters was measured at Temp = 6.0 C, Pressure = .565 atm

Answer 1

The mass of helium is 5.02 g. The balloon will burst.

Explanation:

Part A. Mass of helium

Step 1. Calculate the moles of helium

At ground level,

`p = 765 color(red)(cancel(color(black)("mmHg"))) × "1 atm"/(760 color(red)(cancel(color(black)("mmHg"))))="1.007 atm"`

`V = "30.0 L"`
`T = "(20 + 273.15) K = 293.15 K"`

`pV = nRT`

`n = (pV)/(RT) = (1.007 color(red)(cancel(color(black)("atm"))) × 30.0 color(red)(cancel(color(black)("L"))))/("0.082 06" color(red)(cancel(color(black)("L·atm·K"^"-1")))"mol"^"-1" × 293.15 color(red)(cancel(color(black)("K")))) = "1.255 mol"`

Step 2. Calculate the mass of helium

`"Mass of He" = 1.255 color(red)(cancel(color(black)("mol He"))) × "4.003 g He"/(1 color(red)(cancel(color(black)("mol He")))) = "5.02 g He"`

Part 2. Calculate the volume at 3000 m

At 3000 m,

`n = "1.255 mol"`
`T = "(6.0 + 273.15) K = 279.15 K"`
`p = "0.565 atm"`

`V = (nRT)/p = (1.255 color(red)(cancel(color(black)("mol"))) ×"0.082 06" "L"color(red)(cancel(color(black)("·atm·K"^"-1""mol"^"-1"))) × 279.15 color(red)(cancel(color(black)("K"))))/(0.565 color(red)(cancel(color(black)("atm")))) = "50.9 L"`

The volume at 3000 m would be more than 47.0 L.

The balloon will burst.