Question

A sample of gas has a volume of 23.0mL at a pressure of 1.45atm. At what pressure will the volume of the sample be equal to 9.5mL?

Answer 1

The final pressure of the sample is 3.5 atm

EXPLANATIONS

Given that;

The initial volume of the sample is 23.0mL

The initial pressure of the sample is 1.45 atm

The final volume of the sample is 9.5mL

To find the final pressure of the sample, follow the steps below

In the given data, the temperature of the sample is fixed. Hence, we can apply Boyle's law to find the final volume

Step 1; state Boyle's law

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

Mathematically, the law can be expressed below

`\begin{gathered} \text{ V }\propto\text{ }(1)/(P) \\ \text{ Introduce a proportionality constant} \\ \text{ V }=\text{ }(k)/(P) \\ \text{ cross multiply} \\ \text{ k }=\text{ PV} \\ P1\text{ V1 }=\text{ P2 V2} \end{gathered}`

Step 2; Substitute the given data into the formula in step 1

`\begin{gathered} \text{ 23 }*\text{ 1.45 }=\text{ P2 }*\text{ 9.5} \\ \text{ 33.35 }=\text{ 9.5 P2} \\ \text{ Divide both sides by 9.5} \\ \text{ }\frac{33.35}{9.5\text{ }}=\text{ }\frac{\cancel{9.5}P2}{\cancel{9.5}} \\ \text{ P2 }=\text{ 3.5 atm} \end{gathered}`

Hence, the final pressure of the sample is 3.5 atm