Question

Question #dd7e8

Answer 1

`"140 atm"`

Explanation:

The trick here is to realize that when volume and number of moles of gas are kept constant, pressure and temperature have a direct relationship as described by Gay Lussac's Law.

In other words, when volume and number of moles are constant, increasing a gas' temperature will cause its pressure to increase, and decreasing the gas' temperature will cause its pressure to decrease.

In your case, the temperature of the gas increases from `"428 K"` to `"684 K"`, which can only mean that its pressure increased as well.

Mathematically, Gay Lussac's Law can be written as

`color(blue)(|bar(ul(color(white)(a/a)P_1/T_1 = P_2/T_2color(white)(a/a)|)))" "`, where

`P_1`, `T_1` - the pressure and temperature of the gas at an initial state
`P_2`, `T_2` - the pressure and temperature of the gas at final state

Rearrange the equation to solve for `P_2`

`P_1/T_1 = P_2/T_2 implies P_2 = T_2/T_1 * P_1`

Plug in your values to find

`P_2 = (684 color(red)(cancel(color(black)("K"))))/(428color(red)(cancel(color(black)("K")))) * "86 atm" = color(green)(|bar(ul(color(white)(a/a)color(black)("140 atm")color(white)(a/a)|)))`

The answer is rounded to two sig figs, the number of sig figs you have for the initial pressure of the gas.