When 1219 J of heat energy is added to 40.4 g of ethanol, C2H6O, the temperature increases by 12.3 °C. Calculate the molar heat capacity of C2H6O. (In J)
q = mass ethanol x specific heat x (Tfinal-Tinitial). This will give you specific heat in J/g. J/g x molar mass will give J/mol.
To calculate the molar heat capacity of C2H6O (ethanol), we need to use the equation:
q = mcΔT
Where:
- q represents the heat energy (in J)
- m represents the mass of the substance (in g)
- c represents the specific heat capacity (in J/g·°C)
- ΔT represents the change in temperature (in °C)
Given:
- Heat energy (q) = 1219 J
- Mass (m) = 40.4 g
- Change in temperature (ΔT) = 12.3 °C
First, we need to convert the mass of ethanol to moles. To do this, we need to divide the mass by the molar mass of ethanol.
The molar mass of ethanol (C2H6O):
(2 x atomic mass of carbon) + (6 x atomic mass of hydrogen) + (1 x atomic mass of oxygen)
= (2 x 12.01 g/mol) + (6 x 1.01 g/mol) + (1 x 16.00 g/mol)
= 46.07 g/mol
Now, we can calculate the moles of ethanol using the mass and molar mass:
moles = mass / molar mass
moles = 40.4 g / 46.07 g/mol
moles ≈ 0.878 mol
Next, we can rearrange the equation q = mcΔT to solve for c:
c = q / (m × ΔT)
Plugging in the values:
c = 1219 J / (40.4 g × 12.3 °C)
c ≈ 2.49 J/g·°C
Therefore, the molar heat capacity of C2H6O (ethanol) is approximately 2.49 J/mol·°C.