Question

4.At a pressure of 1.0 atm, a sample of oxygen gas in a balloon occupies 4.0 L.a.If the pressure is increased to 2.0 atm and the temperature remains constant, will the volume of the balloon increase or decrease?b.Which gas law does this demonstrate?

Answer 1

The final volume of the ballon is 2.0L

Explanation:

What to find? The final volume of the balloon

Given parameters

The initial pressure of the oxygen gas = 1.0 atm

The initial volume = 4.0 L

The final pressure of the gas = 2.0 atm

To find the final volume of the gas, we will need to apply Boyle's law

Boyle's law states that the volume of a given gas is inversely proportional to its pressure provided that the temperature remains constant.

This law can be expressed mathematically below

`\begin{gathered} P\text{ }\propto\text{ }(1)/(V) \\ \text{Introducing a proportionality constant} \\ P\text{ = }\frac{K\cdot\text{ 1}}{V} \\ P\text{ = }(K)/(V) \\ \text{ introduce cross multiply} \\ K\text{ = PV} \\ \text{where k = temperature and it is constant} \\ P1V1\text{ = P2V2} \end{gathered}`

The next step is to substitute the parameters into the formula

`\begin{gathered} P1\text{ = 1.0 atm} \\ V1\text{ = 4.0L} \\ P2\text{ = 2.0 atm} \\ V2\text{ =?} \\ 1\cdot\text{ 4 = 2 }\cdot\text{ V2} \\ 4\text{ = 2V2} \\ \text{Divide both sides by 2} \\ (4)/(2)\text{ = }(2V2)/(2) \\ V2\text{ = }(4)/(2) \\ V2\text{ = 2.0L} \\ \text{Hence, the final volume of the balloon is 2.0L} \end{gathered}`

According to the above calculations, we observed that there is a decrease in the volume of the ballon

PART B

The gas law demonstrated is Boyle's law