A 2.75 g sample of the hydrocarbon acetone, CH3COCH3, is burned in a bomb calorimeter with 975 mL of water, initially at 23.50 degrees celsius. The bomb is constructed of 285.0 g of nickel metal having a specific heat capacity of Cp = 0.826 J/ g degrees C. The final temperature of the bomb and the water after the combustion process increases to 29.55 degrees celsius. calculate the following:
(a)The heat flow at constant volume, qv for this combustion (in kJ/mol).
i know qv = delta E. and that delta E = q + w. but how do i find the work? i know work = force / distance. (i'm sorry if i sound incompetent but i'm struggling because my book gives an example where the work is already given so it is not helpful at all.)
(b)The energy released per mole of acetone (in kj/mole).
(c)calculation (b) amounts to the heat of combustion per mole, delta h comb/mole for this compound. Balance the reaction for the complete combustion of acetone, find delta n and then find the value of delta H per mole of acetone (kJ/mole).
i don't know how to even start part (b).
To find the work done in this combustion process, we need to consider the bomb calorimeter as a closed system. In this case, the work done is zero because there is no volume change. Therefore, the formula becomes:
ΔE = q + 0
qv = ΔE
Now let's calculate the heat flow at constant volume:
(a) The heat flow at constant volume, qv, can be calculated using the formula:
qv = ΔE
To find ΔE, we need to consider the heat absorbed by the water and the heat absorbed by the nickel bomb calorimeter. The heat absorbed by the water can be calculated using the formula:
qwater = mcΔT
where:
m = mass of water = 975 mL = 975 g (since the density of water is 1 g/mL)
c = specific heat capacity of water = 4.184 J/g°C (approximate value)
ΔT = change in temperature = final temperature - initial temperature = 29.55°C - 23.50°C = 6.05°C
Substituting the values into the equation:
qwater = (975 g) (4.184 J/g°C) (6.05°C)
Next, we need to calculate the heat absorbed by the nickel bomb calorimeter. The heat absorbed by the nickel bomb calorimeter can be calculated using the formula:
qcalorimeter = mcΔT
where:
m = mass of nickel = 285.0 g
c = specific heat capacity of nickel = 0.826 J/g°C (given)
ΔT = change in temperature = final temperature - initial temperature = 29.55°C - 23.50°C = 6.05°C
Substituting the values into the equation:
qcalorimeter = (285.0 g) (0.826 J/g°C) (6.05°C)
Finally, we can find the total heat flow at constant volume:
qv = qwater + qcalorimeter
Substitute the calculated values and calculate qv.
(b) The energy released per mole of acetone, in kJ/mol, can be found by dividing the heat flow at constant volume by the number of moles of acetone burned.
To calculate the number of moles of acetone burned, we need to use the molar mass of acetone, which is 58.08 g/mol.
Number of moles = mass of acetone (g) / molar mass of acetone (g/mol)
Substitute the given mass of the hydrocarbon acetone and the molar mass into the formula, and calculate the number of moles.
Now, divide the heat flow at constant volume (qv) by the number of moles of acetone to get the energy released per mole of acetone.
(c) To calculate the heat of combustion per mole, ΔH_comb/mole, we need to balance the equation for the combustion of acetone.
The balanced equation for the complete combustion of acetone is:
2CH3COCH3 + 9O2 → 6CO2 + 8H2O
The ΔH_comb/mole can be calculated using the formula:
ΔH_comb/mole = qv / number of moles of acetone burned
Substitute the calculated qv and the number of moles of acetone burned into the formula, and calculate ΔH_comb/mole.
No worries, I can help you break down the problem and guide you through the calculations.
(a) To find the work, we first need to understand that in this case, the bomb calorimeter operates at constant volume. This means that the system doesn't do any work on its surroundings, so the work done (w) is zero. Therefore, the change in internal energy (delta E) is equal to the heat flow at constant volume (qv), as you mentioned.
Now, we can calculate delta E using the equation:
delta E = q + w
Since w is zero, we can simplify the equation to:
delta E = qv
We can rearrange the equation to solve for qv:
qv = delta E
To find delta E, we need to calculate the change in enthalpy (delta H) of the reaction. We can use the equation:
delta H = qrxn
The change in enthalpy of the reaction is equal to the heat released (qrxn) in this case, as no work is done.
Now, let's move on to finding the energy released per mole of acetone.
(b) To calculate the energy released per mole of acetone, we need to determine the number of moles of acetone burned and then divide the total energy released (qv) by that number of moles.
1. Calculate the moles of acetone:
To find the number of moles, we need to use the molar mass of acetone (CH3COCH3), which is 58.08 g/mol.
Moles of acetone = mass of acetone / molar mass
Moles of acetone = 2.75 g / 58.08 g/mol
2. Calculate the energy released per mole:
Energy released per mole of acetone = qv / Moles of acetone
Since you're given qv in kJ/mol, you can directly divide qv by Moles of acetone to obtain the energy released per mole in kJ/mol.
(c) To determine the heat of combustion per mole, delta Hcomb/mole for acetone, we need to balance the reaction for the complete combustion of acetone, find the change in moles (delta n), and then use that to calculate delta H per mole.
The balanced chemical equation for the complete combustion of acetone is:
CH3COCH3 + 4O2 -> 3CO2 + 3H2O
Now, since 1 mol of acetone produces 3 moles of CO2, the change in moles (delta n) is equal to 3 moles.
delta Hcomb/mole = Energy released per mole of acetone / delta n
I hope this helps you understand how to solve the given problem. Let me know if you have any further questions!