Question

A gas occupies 11.2 liters at 0.860 atm. What is the pressure if the volume becomes 15.0 L? (Boyle)

Answer 1

Given:

Initial Volume
`\sf (V_1)` = 11.2 L

Initial Pressure
`\sf (P_1)` = 0.860 atm

Final Volume
`\sf (V_2)` = 15.0 L

To Find:

Final Pressure
`\sf (P_2)`

Concept/Theory:

`\bf{ \underline{Boyle's \: Law} \: (Pressure - Volume \: Relationship)}`

"At constant temperature, the pressure of a fixed amount of gas varies inversely with the volume of the gas."

`\bf{P \propto (1)/(V) \: (at \: constant \: T \: and \: n)}`

It can be also stated as "At constant temperature, the product of pressure and volume of fixed amount of a gas remains constant."

`\bf{PV = Constant}`

If the initial pressure and volume of a fixed amount of gas at constant temperature are
`\sf (P_1)` &
`\sf (V_1)` and final pressure of the gas is
`\sf (P_2)` and volume occupied is
`\sf (V_2)`, then according to Boyle's law;

`\bf{P_1V_1 = P_2V_2 = Constant}`

OR

`\bf{(P_1)/(P_2) = (V_2)/(V_1)}`

Answer:

By using Boyle's Law, we get:

`\rm \longrightarrow (0.860)/(P_2) = (15.0)/(11.2) \\ \\ \rm \longrightarrow P_2 = (11.2)/(15.0) * 0.860 \\ \\ \rm \longrightarrow P_2 = (9.632)/(15.0) \\ \\ \rm \longrightarrow P_2 = 0.642 \: atm`

`\therefore` Final Pressure
`\sf (P_2)` = 0.642 atm

Answer 2

0.642 atm

Step-by-step explanation:

The new pressure can be found by using the formula for Boyle's law which is

`P_1V_1 = P_2V_2`

Since we are finding the new pressure

`P_2 = (P_1V_1)/(V_2) \\`

From the question we have

`P_2 = (11.2 * 0.86)/(15) = (9.632)/(15) \\ = 0.64213333...`

We have the final answer as

0.642 atm

Hope this helps you