When one mole of C6H6 is burned, 5.69 MJ of heat is produced. When the heat from burning 9.69 g of C6H6 is added to 5.69 kg of water at 21.0°C, what is the final temperature of the water?
heat produced by burning 9.69g C6H6 is
5.69 mJ/mol x (9.69/molar mass C6H6) = ? MJ. Convert to J. Then
J = mass H2O in g x specific heat H2O x (Tfinal-Tintial) and solve for Tf.
To find the final temperature of the water, we need to use the heat gained by the water and equate it to the heat released by burning C6H6.
First, let's find the heat gained by the water using the formula:
Q = m * c * ΔT
Where:
Q = heat gained by the water (in joules)
m = mass of water (in kilograms)
c = specific heat capacity of water (4.18 J/g°C or 4.18 J/kg°C)
ΔT = change in temperature of water (final temperature - initial temperature)
Given:
Mass of water (m) = 5.69 kg
Specific heat capacity of water (c) = 4.18 kJ/kg°C (convert from J/g°C to J/kg°C)
Initial temperature = 21.0°C
Now, let's calculate the heat gained by the water:
Q = m * c * ΔT
Q = 5.69 kg * 4.18 kJ/kg°C * ΔT
Next, let's find the heat released by burning C6H6. Since 1 mole of C6H6 produces 5.69 MJ of heat, we need to calculate the number of moles of C6H6 burned.
Given:
Mass of C6H6 burned = 9.69 g
Molar mass of C6H6 = 78.11 g/mol
Number of moles of C6H6 = mass / molar mass
Number of moles of C6H6 = 9.69 g / 78.11 g/mol
Once we have the number of moles of C6H6 burned, we can calculate the heat released:
Heat released by burning C6H6 = number of moles * heat released per mole
Now, we can equate the heat gained by the water to the heat released by burning C6H6:
Heat gained by water = Heat released by C6H6
5.69 kg * 4.18 kJ/kg°C * ΔT = number of moles * heat released per mole
Now we can solve for ΔT, which is the change in temperature of the water, and find the final temperature by adding it to the initial temperature.