Question

What is the resulting temperature if a sample of gas began with a temperature of 20 C, 1 liter, and 760 mmHg and now occupies 800 mL and has a pressure of 1000 mmHg?

Answer 1

`T_2 = 317` `"K"`

Explanation:

We're asked to find the new temperature of a gas after it is subjected to changes in pressure and volume.

To do this, we can use the combined gas law:

`ulbar(|stackrel(" ")(" "(P_1V_1)/(T_1) = (P_2V_2)/(T_2)" ")|)`

where

• `P_1` is the original pressure (given as `760` `"mm Hg"`)

• `V_1` is the original volume (given as `1` `"L"`)

• `T_1` is the original absolute temperature, which is

`20` `""^"o""C"` `+ 273 = ul(298color(white)(l)"K"`

• `P_2` is the final pressure (given as `1000` `"mm Hg"`)

• `V_2` is the final volume (given as `800` `"mL"` `= ul(0.800color(white)(l)"L"`) (units must be consistent, so convert this to liters)

• `T_2` is the final absolute temperature* (what we're trying to find***)

Let's rearrange this equation to solve for the final temperature, `T_2`:

`T_2 = (P_2V_2T_1)/(P_1V_1)`

Plugging in the above values:

`T_2 = ((1000cancel("mm Hg"))(0.800cancel("L"))(298color(white)(l)"K"))/((760cancel("mm Hg"))(1cancel("L"))) = color(red)(ulbar(|stackrel(" ")(" "317color(white)(l)"K"" ")|)`

The final temperature of the gas is thus `color(red)(317` `sfcolor(red)("kelvin"`.