# 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?

Mar 14, 2016

The molar heat capacity of ethanol is $\text{107 J·°C"^"-1""mol"^"-1}$.

#### 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)

$q = \text{2211 J}$

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,

$q = \text{2211 J"/("1.035 mol" × "19.9 °C") = "107 J·°C"^"-1""mol"^"-1}$

The molar heat capacity of ethanol is $\text{107 J·°C"^"-1""mol"^"-1}$.