Question #dd7e8

1 Answer
Jun 27, 2016

Answer:

#"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.

https://www.emaze.com/@ALCFZRWL/Gay-Lussac's-Law

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.