Question #542e5

1 Answer
May 30, 2017

Here's what I got.

Explanation:

The idea here is that the volume of a gas is directly proportional to its temperature when the number of moles of gas and the pressure of the gas are kept constant #-># this is known as Charles' Law.

In other words, when pressure and the number of moles of gas are kept constant, decreasing the temperature by a factor #f# will cause its volume to decrease by the same factor #f#.

In your case, the volume decreased

#"240 mL " -> " 180 mL"#

which implies that the temperature decreased as well

#"270 K " -> " ? K"#

Now, the volume decreased by a factor

#(240 color(red)(cancel(color(black)("mL"))))/(180color(red)(cancel(color(black)("mL")))) = color(blue)(4/3)#

You can thus say that the temperature of the gas decreased by a factor of #color(blue)(4/3)# as well, so

#f = "270 K"/"final temperature"#

which means that

#"final temperature" = "270 K"/color(blue)(4/3) = "202.5 K"#

Rounded to two sig figs, the answer will be

#color(darkgreen)(ul(color(black)("final temperature" = 2.0 * 10^2color(white)(.)"K")))#