# 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.

##### 1 Answer

#### 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* **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

#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**.