Question

If the heat of combustion of ethanol is $1367kJmo{l^{ - 1}}$ , how would you calculate the theoretical mass of ethanol required to heat $200mL$ of water from ${21.0^0}$ to ${45^0}$ ?

Answer 1

Hint:To solve this question we must apply the formula for specific heat capacity or also called as specific heat. First we need to know what specific heat capacity is. Heat capacity of a substance is the quantity of the heat which is required to raise the temperature of the entire substance by one degree. If the mass of the substance is unity then the heat capacity is called a specific heat capacity or the specific heat.

Complete step-by-step answer: In order to solve this problem first we must find out how much energy is involved in heating the water.
For that the energy equation is given as
$E = m \cdot c \cdot \theta $
Where, E is the energy we have to find out which is in Joules.
m is the mass in kilograms, so we have to convert $200mL$ to kilograms therefore $200$divided by $1000$ hence we must substitute $0.2kg$
c is the specific heat of water which is $4186J/kg$
$\theta $ is the temperature increase which is the difference between ${45^0}$ and ${21.0^0}$ which is ${24^0}$
Thereby by substituting the values we get,
\[\
  E{\text{ }} = {\text{ }}0.2 \times 4186 \times 24 = 20,092.8{\text{ }}J \\
   = 20.092kJ \\
\ \]
As given in the question one mole of ethanol when combusted releases \[1367{\text{ }}kJ\] of energy.
Hence to obtain \[20.0928{\text{ }}kJ\]we need,\[\dfrac{{20.0928}}{{1367}} = 0.0147moles\]
Molar mass of ethanol is \[46.07{\text{ }}g/mol\], therefore we need \[0.0147 \times 46.07{\text{ }} = {\text{ }}0.68{\text{ }}g\]of ethanol.
Therefore the theoretical mass of ethanol is $0.68g$

Note:Specific heat is usually used when we are referring to something in particular. Heat capacity is defined as the ratio of the quantity of heat required to alter the temperature by one degree Celsius. But when we consider a certain amount of mass we use Specific Heat or Specific Heat Capacity. The heat capacity of most systems is not constant and it depends on factors like the pressure, volume and temperature.