Question

In: Chemistry

A balloon filled with 6.50 L He rises from sea level to a height where the...

A balloon filled with 6.50 L He rises from sea level to a height where the pressure is 700 mm Hg. Would the volume of the gas in the balloon be greater than, equal to, or less than at sea level? Also, can you explain why?

Solutions

Expert Solution

When the balloon is filled with He at sea level we can find the amount of He in it using the formula. Here pressure is 760 mmHg which is 1 atm, assuming 25 oC which is 298 K

PV=nRT

1 atm x 6.5 L = n x 0.082057 L atm K−1 mol−1 x 298 K

n = (1 atm x 6.5 L)/0.082057 L atm K−1 mol−1 x 298 K

n = 0.266 moles of He

Now when it rises from sea level to a height where the pressure is 700 mm Hg that is 0.921 atm the number of moles remains the same.

PV= nRT

0.921 atm x V = 0.266mol x 0.082057 L atm K−1 mol−1 x 298 K

V = (0.266 mol x 0.082057 L atm K−1 mol−1 x 298 K)/0.921 atm

V = 7.057 L

So the volume of gas in the ballon will be greater than that at sea level

This is well explained by Boyle's law which states

The absolute pressure exerted by a given mass of an ideal gas is inversely proportional to the volume it occupies if the temperature and amount of gas remain unchanged within a closed system.

Mathematically, Boyle's law can be stated as

So when pressure decreases volume increases


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