Question

Question #542e5

Answer 1

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")))`