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#?

1 Answer
Mar 14, 2016

Answer:

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"#.