Call

We can use here the , relating the temperature, pressure, and volume of a gas with a constant quantity:

$(P_1V_1)/(T_1) = (P_2V_2)/(T_2)$

If you're using the ideal-gas equation, which we're NOT using here, you would have to convert each measurement into the appropriate units ($"L", "K", "atm",$and $"mol"$). The only measurement that needs conversion here is temperature, from $"^oC$ to $"K"$. (You will always convert temperature to Kelvin (absolute temperature) when using gas equations).

The Kelvin temperature is

$"K" = 20^(o)C + 273 = 293"K"$

Let's rearrange the combined gas law to solve for the final temperature, $T_2$:

$T_2 = (P_2V_2T_1)/(P_1V_1)$

Plugging in known values, we can find the final temperature:

$T_2 = ((56.7"kPa")(8.00"L")(293"K"))/((86.7"kPa")(3.50"L")) = 438"K"$

Lastly, we'll convert back from $"K"$ to $"^oC$:

$438"K" - 273 = color(blue)(165^oC$