Question

How do you calculate the mass of ethanol that must be burnt to increase the temperature of `210 g` of water by `65^@`, if exactly half of the heat released by this combustion is lost to the surroundings?

The heat of combustion of ethanol is `1367 kJmol^-1`.

Answer 1

You must burn 3.8 g of ethanol.

Explanation:

Step 1. Calculate the theoretical amount of heat required

The formula for the quantity of heat `q` transferred is

`color(blue)(bar(ul(|color(white)(a/a)q = mC_text(s)ΔTcolor(white)(a/a)|)))" "`

where

`m color(white)(ll) =` the mass of the object
`C_text(s) color(white)(l) =` its specific heat capacity
`ΔT =` its change in temperature

In this problem,

`m color(white)(ll)= "210 g"`
`C_text(s) color(white)(ll)= "4.184 J·°C"^"-1""g"^"-1"`
`ΔT = "65 °C"`

`q = 210 color(red)(cancel(color(black)("g"))) × 4.184 "J"·color(red)(cancel(color(black)("°C"^"-1""g"^"-1"))) ×65 color(red)(cancel(color(black)("°C"))) = "57 100"color(white)(l)"J" = "57.1 kJ"`

Step 2. Calculate the actual amount of heat required

`"Heat required" = 57.1 color(red)(cancel(color(black)("kJ theoretical"))) × "2 kJ required"/(1 color(red)(cancel(color(black)("kJ theoretical")))) = "114 kJ"`

Step 3. Calculate the moles of ethanol required

The equation for the combustion of ethanol is

`"C"_2"H"_5"OH" + "⁷/₂O"_2 → "2CO"_2 + "3H"_2"O" + "1367 kJ"`

`"Theoretical moles" = 114 color(red)(cancel(color(black)("kJ"))) × "1 mol ethanol"/(1367 color(red)(cancel(color(black)("kJ")))) = "0.0836 mol ethanol"`

Step 4. Calculate the mass of ethanol

`"Mass of ethanol" = 0.0836 color(red)(cancel(color(black)("mol ethanol"))) × "46.07 g ethanol"/(1 color(red)(cancel(color(black)("mol ethanol")))) = "3.8 g ethanol"`