Question

A 20. L container is filled with helium and the pressure is 150 atm and the temperature is 30. C. How many 5.0L balloons can be filled when the
temperature is 22 C and the atmospheric pressure is 755 mmHg.

Answer 1

Considering the combined law equation, 2940.13 L can be filled when the temperature is 22 C and the atmospheric pressure is 755 mmHg.

Gay-Lussac's law

Gay-Lussac's law states that when there is a constant volume, as the temperature increases, the pressure of the gas increases. And when the temperature is decreased, gas pressure decreases. That is, the pressure of the gas is directly proportional to its temperature.

Gay-Lussac's law can be expressed mathematically as follows:

$\frac{P}{T} =k$

Boyle's law

On the other hand, Boyle's law says that the volume occupied by a given mass of gas at constant temperature is inversely proportional to the pressure. That is, if the pressure increases, the volume decreases; while if the pressure decreases, the volume increases.

Boyle's law is expressed mathematically as:

P×V=k

Charles's Law

Finally, Charles's Law states that for a given sum of gas at constant pressure, as the temperature increases, the volume of the gas increases and as the temperature decreases, the volume of the gas decreases. That is, the volume is directly proportional to the temperature of the gas.

Mathematically, Charles's law expresses that:

$\frac{V}{T} =k$

Combined law equation

Combined law equation is the combination of three gas laws called Boyle's, Charlie's and Gay-Lusac's law:

$\frac{PxV}{T} =k$

Studying an initial state 1 and a final state 2, the following is fulfilled:

$\frac{P1xV1}{T1} =\frac{P2xV2}{T2}$

Final volume

In this case, you know:

• P1= 150 atm
• V1= 20 L
• T1= 30 C= 303 K (being 0 C= 273 K)
• P2= 755 mmHg= 0.993421 atm (being 760 mmHg= 1 atm)
• V2= ?
• T2= 295 K

Replacing in the combined law equation:

$\frac{150 atmx20 L}{303 K} =\frac{0.993421 atmxV2}{295 K}$

Solving:

$\frac{150 atmx20 L}{303 K}\frac{295 K}{0.993421atm} =V2$

2940.13 L= V2

Finally, 2940.13 L can be filled when the temperature is 22 C and the atmospheric pressure is 755 mmHg.

Learn more about combined law equation:

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