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.
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
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)))#
#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.