Question

A sample of carbon dioxide gas at a pressure of 1.07 atm and a temperature of 166 °C, occupies a volume of 686 mL. If the gas is heated at constant pressure until its volume is 913 mL, the temperature of the gas sample will be ? °C.

Answer 1

`311^@"C"`

Explanation:

The idea here is that the volume and the temperature of a gas have a direct relationship when the pressure and the number of moles of gas are being kept constant `->` this is known as Charles' Law.

A very important thing to remember is that the temperature of the gas must be expressed in Kelvin. In other words, you must always work with the absolute temperature of a gas.

So, start by converting the temperature of the gas to Kelvin by using

`color(blue)(ul(color(black)(T["K"] = t[""^@"C"] + 273.15)))`

You will have

`T = 166^@"C" + 273.15 = "439.15 K"`

The volume of the gas will increase as temperature increases and decrease as temperature decreases. Mathematically, this can be written as

`color(blue)(ul(color(black)(V_1/T_1 = V_2/T_2)))`

Here

• `V_1` and `T_1` represent the volume and the temperature of the gas at an initial state
• `V_2` and `T_2` represent the volume and the temperature of the gas at a final state

Rearrange the equation to solve for `T_2`

`V_1/T_1 = V_2/T_2 implies T_2 = V_2/V_1 * T_1`

Plug in your values to find

`T_2 = (913 color(red)(cancel(color(black)("mL"))))/(686color(red)(cancel(color(black)("mL")))) * "439.15 K" = "584.47 K"`

Finally, convert this to degrees Celsius

`color(darkgreen)(ul(color(black)(t[""^@"C"] = "584.47 K" - 273.15 = 311^@"C")))`

The answer is rounded to three sig figs.