The molar enthalpy of combustion of ethanol is -1234.8kJ/mol. How much water can be heated from 10.85 degrees celsius to 72.6 degrees celsius by the combustion of 42.2 g of ethanol.
To solve this problem, we need to use the equation:
q = mcΔT
Where:
q = heat energy absorbed by water (in joules)
m = mass of water (in grams)
c = specific heat capacity of water (4.18 J/g°C)
ΔT = change in temperature (final temperature - initial temperature) (in °C)
First, let's calculate the moles of ethanol burned:
1 mole of ethanol = 46.07 g
42.2 g of ethanol = 42.2 g / 46.07 g/mol = 0.9162 mol of ethanol
Next, we will calculate the heat energy released by the combustion of 1 mole of ethanol:
Molar enthalpy of combustion of ethanol = -1234.8 kJ/mol
Since 1 kJ = 1000 J, the molar enthalpy in joules is:
-1234.8 kJ/mol = -1234.8 x 1000 J/mol = -1,234,800 J/mol
Now, let's calculate the heat energy released by the combustion of 0.9162 mol of ethanol:
Heat energy released by combustion = -1,234,800 J/mol x 0.9162 mol = -1,131,259.76 J
Next, let's calculate the mass of water:
Mass of water = density of water x volume of water
As the volume of water is not given, we will assume it to be 1 liter (1000 grams) for this calculation.
Mass of water = 1000 grams
Finally, let's calculate the change in temperature:
ΔT = final temperature - initial temperature = 72.6°C - 10.85°C = 61.75°C
Now, let's calculate the heat energy absorbed by the water:
q = mcΔT
q = 1000 g x 4.18 J/g°C x 61.75°C = 258,695 J
Since the negative sign in the molar enthalpy of combustion indicates that heat is being released, we need to reverse the sign of the heat energy released by the combustion:
Heat energy released by combustion = -(-1,131,259.76 J) = 1,131,259.76 J
Finally, let's calculate the amount of water that can be heated:
Mass of water heated = q / heat energy released by combustion
Mass of water heated = 258,695 J / 1,131,259.76 J = 0.2286
Therefore, approximately 0.23 kg (or 230 grams) of water can be heated from 10.85°C to 72.6°C by the combustion of 42.2g of ethanol.
To solve this problem, we can use the equation:
q = m × C × ΔT
where:
q is the heat energy gained by the water in Joules (J),
m is the mass of the water in grams (g),
C is the specific heat capacity of water (4.18 J/g°C), and
ΔT is the temperature change in degrees Celsius (°C).
First, let's calculate the mass of water using the given temperature change and the specific heat capacity of water.
ΔT = (72.6°C - 10.85°C) = 61.75°C
Now, let's calculate the heat energy gained by the water.
q = m × C × ΔT
q = (mass of water) × (specific heat capacity of water) × (temperature change)
q = m × 4.18 J/g°C × 61.75°C
Now, we need to calculate the mass of water in grams. The heat energy released by the combustion of ethanol is equal to the heat energy gained by the water. We can use the molar enthalpy of combustion of ethanol (-1234.8 kJ/mol) to find the heat energy.
First, convert the mass of ethanol to moles using the molar mass of ethanol.
The molar mass of ethanol (C2H5OH) is:
2 × atomic mass of carbon (C) + 6 × atomic mass of hydrogen (H) + atomic mass of oxygen (O)
= (2 × 12.01 g/mol) + (6 × 1.01 g/mol) + (16.00 g/mol)
= 46.07 g/mol
Now, let's calculate the number of moles.
moles of ethanol = (mass of ethanol) ÷ (molar mass of ethanol)
moles of ethanol = 42.2 g ÷ 46.07 g/mol
Next, let's calculate the heat energy in Joules.
Heat energy = moles of ethanol × molar enthalpy of combustion of ethanol
However, the molar enthalpy of combustion of ethanol is given in kJ/mol. We need to convert it to J/mol by multiplying by 1000 since 1 kJ = 1000 J.
Molar enthalpy of combustion of ethanol = -1234.8 kJ/mol × 1000 J/kJ
Finally, we can equate the heat energy gained by the water to the heat energy released by the combustion of ethanol.
(q) = (mass of water) × 4.18 J/g°C × 61.75°C
Heat energy = (moles of ethanol) × (molar enthalpy of combustion of ethanol)
Now, we can solve for the mass of water.
(mass of water) = [(moles of ethanol) × (molar enthalpy of combustion of ethanol)] ÷ (4.18 J/g°C × 61.75°C)
Substituting all the known values into the equation will give us the final answer.
To calculate the amount of water that can be heated, we need to use the equation:
q = mcΔT
where q is the heat energy absorbed by the water, m is the mass of water, c is the specific heat capacity of water, and ΔT is the change in temperature.
First, we need to calculate the heat energy released by the combustion of 42.2 g of ethanol. The molar mass of ethanol (C2H5OH) is calculated as follows:
C (12.01 g/mol) * 2 + H (1.008 g/mol) * 6 + O (16.00 g/mol) + H (1.008 g/mol) = 46.07 g/mol
Next, we can calculate the moles of ethanol burned using the molar mass and mass given:
moles of ethanol = mass / molar mass
= 42.2 g / 46.07 g/mol
Now, we can calculate the heat energy released during the combustion of ethanol:
heat energy released = moles of ethanol * molar enthalpy of combustion
= (42.2 g / 46.07 g/mol) * -1234.8 kJ/mol
Next, we need to calculate the amount of heat energy absorbed by the water using the equation mentioned earlier. The specific heat capacity of water (c) is approximately 4.18 J/g·°C.
To convert the heat energy from kilojoules (kJ) to joules (J), we multiply heat energy released by 1000:
heat energy released in joules = (42.2 g / 46.07 g/mol) * -1234.8 kJ/mol * 1000 J/1 kJ
Now, we can calculate the mass of water using the equation:
heat energy released in joules = mass of water * specific heat capacity * ΔT
Rearranging the equation, we get:
mass of water = heat energy released / (specific heat capacity * ΔT)
mass of water = heat energy released in joules / (4.18 J/g·°C * (72.6 - 10.85) °C)
Now we can substitute the values to calculate the mass of water:
mass of water = (42.2 g / 46.07 g/mol) * -1234.8 kJ/mol * 1000 J/1 kJ / (4.18 J/g·°C * (72.6 - 10.85) °C)
mass of water = 65.275 g
Therefore, approximately 65.275 grams of water can be heated from 10.85°C to 72.6°C by the combustion of 42.2 grams of ethanol.