Question

When 2211 J of heat energy is added to 47.7 g of ethanol, `C_2H_6O`, the temperature increases by 18.9°C. What is the molar heat capacity of `C_2H_6O`?

Answer 1

The molar heat capacity of ethanol is `"107 J·°C"^"-1""mol"^"-1"`.

Explanation:

A typical calorimetry formula for calculating the molar heat capacity of a substance is

`color(blue)(|bar(ul( q = ncΔT)|)`

where

• `q` = amount of heat transferred
• `n` = number of moles
• `c` = molar heat capacity
• `ΔT` = change in temperature

We can rearrange this formula to

`c = q/(nΔT)`

In your problem,

`q = "2211 J"`

`n = 47.7 color(red)(cancel(color(black)("g C"_2"H"_6"O"))) × ("1 mol C"_2"H"_6"O")/(46.07 color(red)(cancel(color(black)("g C"_2"H"_6"O")))) = "1.035 mol C"_2"H"_6"O"`

`ΔT = "19.9 °C"`

Hence,

`q = "2211 J"/("1.035 mol" × "19.9 °C") = "107 J·°C"^"-1""mol"^"-1"`

The molar heat capacity of ethanol is `"107 J·°C"^"-1""mol"^"-1"`.