# A sample of ideal gas at room temperature occupies a volume of 17.0L at a pressure of 822torr . If the pressure changes to 4110torr , with no change in the temperature or moles of gas, what is the...

A sample of ideal gas at room temperature occupies a volume of 17.0L at a pressure of 822torr . If the pressure changes to 4110torr , with no change in the temperature or moles of gas, what is the new volume, V2?

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We can use the Boyle’s law in order to solve the problem. We know that pressure is inversely proportional to the volume of the gas. Having said that, the expression can be written as:

`(P_1)*(V_1) = (P_2)*(V_2) `

Where:

`P_1` = 822 Torr

`P_2` = 4110 Torr

`V_1` = 17.0 L

`V_2` = ?

Substitute the values and solve for `V_2`

`(P_1)*(V_1) = (P_2)*(V_2)`

`V_2 = (P_1*V_1)/(P_2) `

`V_2 = (822*17.0)/(4110) `

`V_2 = 3.40 L` -> answer

The final volume (`V_2` ) should decrease because the applied pressure (`P_2` ) increases.

With temperature being constant, you are dealing with Boyle's Law. When pressure goes up, volume goes down. Similarly, when volume goes up, pressure goes down.

`P_1V_1 = P_2V_2`

Plug in your known values.

`(822)(17) = (4110)V_2`

And solve for your unknown.

`13974 = 4110V_2`

`V_2 = 3.4 "L"`

Since all your given values have three sig figs, so should your answer. Therefore, the final answer is:

`V_2 = 3.40 "L"`