# 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.

Apr 4, 2017

${311}^{\circ} \text{C}$

#### 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 $\to$ 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

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{T \left[\text{K"] = t[""^@"C}\right] + 273.15}}}$

You will have

$T = {166}^{\circ} \text{C" + 273.15 = "439.15 K}$

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

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{{V}_{1} / {T}_{1} = {V}_{2} / {T}_{2}}}}$

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 ${T}_{2}$

${V}_{1} / {T}_{1} = {V}_{2} / {T}_{2} \implies {T}_{2} = {V}_{2} / {V}_{1} \cdot {T}_{1}$

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.