Question #d0747
1 Answer
Here's what I got.
Explanation:
The idea here is that the volume of a gas varies directly with its temperature when the number of moles of gas and the pressure are kept constant
You can describe this 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
In your case, the volume of the gas is increasing
#"0.43 mL " ->" 1 mL"#
which means that the temperature must have increased.
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 = (1 color(red)(cancel(color(black)("mL"))))/(0.43color(red)(cancel(color(black)("mL")))) * "299 K" = "695.3 K"#
To convert this to degrees Celsius, use the fact that
#color(blue)(ul(color(black)(t[""^@"C"] = T["K"]- 273.15)))#
You will end up with
#t[""^@"C"] = "695.3 K" - 273.15 = color(darkgreen)(ul(color(black)(420^@"C")))#
I'll leave the answer rounded to two sig figs, but keep in mind that only have one significant figure for the second volume of the gas.