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 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).
thank you!
To solve this problem, we can use the formula:
qv = q + w
where qv is the heat flow at constant volume, q is the heat transferred to the system, and w is the work done by the system.
(a) Finding the work done:
At constant volume, the volume of the system remains constant. Therefore, no work is done (w=0). Hence,
qv = q
(b) Energy released per mole of acetone:
To find the energy released per mole of acetone, we need to calculate the heat transferred to the system during combustion. We can use the formula:
q = mcΔT
where q is the heat transferred, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
In this case, the substance is the water. We need to calculate the heat transferred to the water, as the combustion of acetone releases energy that heats up the water.
To find the mass of water in grams, we can use the density of water, which is approximately 1 g/mL:
Mass of water = Volume of water × density of water
Given that the initial volume of water is 975 mL and the density of water is 1 g/mL:
Mass of water = 975 g
Now, we can calculate the heat transferred to the water:
q = mcΔT = (mass of water)(specific heat capacity of water)(change in temperature)
The specific heat capacity of water (c) is approximately 4.18 J/g·°C.
q = (975 g)(4.18 J/g·°C)(29.55 °C - 23.50 °C)
(c) Calculation of energy per mole of acetone:
To calculate the energy per mole of acetone, we need to convert the heat transferred to the water (q) to the heat of combustion per mole of acetone (ΔH_comb). We can use the molar mass of acetone (CH3COCH3), which is approximately 58 g/mol.
To convert q to kJ/mol, divide it by the molar mass of acetone:
Energy released per mole of acetone = (q ÷ molar mass of acetone) / 1000
Since the question asks for the energy released per mole in kJ/mole, we divide by 1000 to convert J to kJ.
Note: The heat released during combustion can be assumed to be the same as the heat absorbed by the water since the bomb calorimeter is isolated from the surroundings.
Let's calculate the values now:
(a) qv = q = (975 g)(4.18 J/g·°C)(29.55 °C - 23.50 °C)
(b) Energy released per mole of acetone = (q ÷ molar mass of acetone) / 1000
(c) Delta H per mole of acetone can be calculated once we have balanced the combustion reaction.
To find the answers to your questions, let's break down the problem into several steps:
Step 1: Calculate the heat absorbed by the water in the calorimeter (qwater)
Since we know the specific heat capacity of water (Cp = 4.18 J/g°C), the mass of the water (975 g), and the change in temperature (ΔT = 29.55°C - 23.50°C = 6.05°C), we can calculate the heat absorbed by the water using the formula:
qwater = Cp × mass × ΔT
Substituting the values, we get:
qwater = 4.18 J/g°C × 975 g × 6.05°C
Step 2: Calculate the heat absorbed by the nickel bomb (qnickel)
Since we know the specific heat capacity of the nickel bomb (Cp = 0.826 J/g°C), the mass of the nickel bomb (285.0 g), and the change in temperature (ΔT = 29.55°C - 23.50°C = 6.05°C), we can calculate the heat absorbed by the nickel bomb using the same formula:
qnickel = Cp × mass × ΔT
Substituting the values, we get:
qnickel = 0.826 J/g°C × 285.0 g × 6.05°C
Step 3: Calculate the total heat flow at constant volume (qv)
The total heat flow at constant volume (qv) can be calculated by summing up the heat absorbed by the water and the nickel bomb:
qv = qwater + qnickel
Step 4: Convert the mass of acetone to moles
We are given the mass of acetone (2.75 g), and to calculate the energy released per mole (kJ/mol), we need to convert the mass to moles. The molar mass of acetone (CH3COCH3) is 58.08 g/mol. So, we divide the mass by the molar mass to get the number of moles:
moles of acetone = mass of acetone (g) / molar mass of acetone (g/mol)
Step 5: Calculate the energy released per mole of acetone (ΔHcomb/mol) and convert to kJ/mol
The energy released per mole of acetone (ΔHcomb/mol) is equal to the total heat flow at constant volume (qv) divided by the number of moles of acetone:
ΔHcomb/mol = qv / moles of acetone
To convert from J/mol to kJ/mol, divide by 1000.
Step 6: Balance the combustion equation for acetone and calculate Δn (change in moles)
The balanced chemical equation for the complete combustion of acetone is:
2 C3H6O(l) + 9 O2(g) → 6 CO2(g) + 6 H2O(l)
From the equation, we can see that the number of moles of acetone consumed is 2 moles per mole of carbon dioxide produced. So, Δn (change in moles) is equal to -2.
Step 7: Calculate the heat of combustion per mole of acetone (ΔHcomb/mol)
The heat of combustion per mole (ΔHcomb/mol) can be calculated by dividing the energy released per mole of acetone (ΔHcomb/mol) by the change in moles (Δn):
ΔHcomb/mol = ΔHcomb/mol / Δn
Now that we have broken down the problem into several steps, you can follow these steps to find the answers to your questions.