Question

Question #d8985

Answer 1

`"4.46 L"`

Explanation:

Before doing ny calculations, try to predict what's going to happen to the volume of the gas.

You know that when pressure and number of moles are kept constant, volume and temperature have a direct relationship.

Simply put, increasing the temperatue will lead to an increase in volume, and decreasing the temperature will lead to a decrease in volume - this is known as Charles' Law.

So, why would that be the case?

Remember that gas pressure is caused by molecules bumpoing into the walls of the container. Temperature as we know it is simply a measure of the average kinetic energy of the molecules that make up the gas sample.

So, higher temperature means that the molecules are moving faster, and thus hitting the walls of the container more often and with more force `->` the volume increases.

Mathematically, Charles' Law is written like this

`color(blue)(V_1/T_1 = V_2/T_2)" "`, where

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

A very important thing to remember here is that temperature must be expressed in Kelvin!

So, plug in your values and solve for `V_2`

`V_2 = T_2/T_1 * V_1`

`V_2 = ((273.15 + 100.0)color(red)(cancel(color(black)("K"))))/((273.15 + 20.0)color(red)(cancel(color(black)("K")))) * "3.50 L" = "4.4551 L"`

Rounded to three sig figs, the answer will be

`V_2 = color(green)("4.46 L")`

Indeed, an increase in temperature lead to an increase in volume!