Question #56270
1 Answer
Explanation:
We're asked to find the final temperature of the gas, given its initial pressure, final pressure, and initial temperature.
We can use GayLussac's law for this problem, which is
#ul((P_1)/(T_1) = (P_2)/(T_2))color(white)(aa)# (constant volume and quantity)
where

#P_1# is the initial pressure 
#P_2# is the final pressure (what we're trying to find) 
#T_1# is the initial absolute temperature (in Kelvin) 
#T_2# is the final absolute temperature (in Kelvin)
We have:

#P_1 = 575# #"torr"# 
#P_2 = 5750# #"torr"# 
#T_1 = 4# #""^"o""C"# #+ 273 = ul(277color(white)(l)"K"# 
#T_2 = ?#
Let's rearrange the above equation to solve for the final temperature,
#T_2 = (T_1P_2)/(P_1)#
Plugging in known values:
#T_2 = ((277color(white)(l)"K")(5750cancel("torr")))/(575cancel("torr")) = color(red)(ul(2770color(white)(l)"K"#
Which, in
#T_2 = color(red)(2770color(white)(l)"K")  273 = color(blue)(ulbar(stackrel(" ")(" "2497color(white)(l)""^"o""C"" "))#