Question

A student is studying a sample of neon in a container with a moveable piston (this means the container can change in size). If the sample in the container is initially at a pressure of 767.7 torr when the container has a volume of 58.1 mL, what is the pressure of the gas when the piston is moved so that the volume of the container becomes 130.3 mL? Round your answer to the nearest 0.01 and include units!

Answer 1

The final pressure of the gas is 342.31 torr

Step-by-step explanation

Given that;

The initial pressure of the gas is 767.7 torr

The initial volume of the container is 58.1 mL

The final volume of the container is 130.3mL

Follow the steps below to find the final pressure of the gas

In the given data, the temperature of the gas is fixed, therefore, we can apply Boyle's law to find the volume

Step 1; States Boyle's law

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

Mathematically

`\begin{gathered} \text{ V }\propto\text{ }\frac{1}{\text{ P}} \\ \text{ Introduce a proportionality constant} \\ \text{ V = }\frac{\text{ k}}{\text{ P}} \\ \text{ cross multiply} \\ \text{ k = PV} \\ \text{ P1 V1 = P2V2} \end{gathered}`

Step 2; Substitute the given data into the above formula

`\begin{gathered} \text{ 767.7 }*\text{ 58.1 = P2 }*\text{ 130.3} \\ \text{ 44603.37 = 130.3 P2} \\ \text{ Divide both sides by 130.3P2} \\ \text{ }\frac{\text{ 44603.37}}{130.3}\text{ = }\frac{\text{ 130.3 P2}}{130.3} \\ \text{ P2 = 342.31 torr} \end{gathered}`

Therefore, the final pressure of the gas is 342.31 torr