1 mole of nitroglycerin decomposes and release 5.72*10^3 KJ heat. to give CO2 H2O O2 and N2.
A) write the balanced chemical equation
B) calculate the work done assuming the temp of the reaction is 450K
4 C3H5(NO3)3(s) --> 12 CO2(g) + 10 H2O(g) + 6 N2(g) + O2(g)
Look up the density of nitroglycerin and calculate the volume of 1 mole. Then count the volume produced by the products. That will be 29 mols O2. Use PV = nRT to convert 29 mols at 450K to volume in L. Then delta V is volume products minus volume reactant.
Work done is -p*(delta V). p is 1 atm.
That will give you the work in L*atm and you can convert to J by multiplying by 101.325.
A) To write a balanced chemical equation for the decomposition of one mole of nitroglycerin, we first need to identify the products. Nitroglycerin decomposes into carbon dioxide (CO2), water (H2O), oxygen (O2), and nitrogen gas (N2). The balanced chemical equation is as follows:
C3H5N3O9 → 3CO2 + 2.5H2O + 1.5O2 + 1.5N2
B) To calculate the work done assuming the temperature of the reaction is 450K, we need to use the formula:
Work done = ΔH - ΔU
ΔH is the enthalpy change of the reaction, which can be calculated using the given heat released:
ΔH = -5.72 * 10^3 kJ/mol
ΔU is the change in internal energy (assuming constant volume, so ΔU = q).
To calculate q, we use the formula:
q = nCΔT
Where n is the number of moles of reaction, C is the molar heat capacity, and ΔT is the change in temperature.
Since we have 1 mole of nitroglycerin, n = 1 mol.
C is the molar heat capacity, which depends on the specific heat capacity of each product. Assuming constant volume, we can use the molar heat capacities at constant volume for each product. For water, carbon dioxide, nitrogen, and oxygen, the molar heat capacities are approximately 33.6 J/(mol·K), 37.1 J/(mol·K), 20.8 J/(mol·K), and 29.4 J/(mol·K), respectively.
Now, we can calculate q:
q = (2.5 mol H2O × 33.6 J/(mol·K)) + (3 mol CO2 × 37.1 J/(mol·K)) + (1.5 mol O2 × 29.4 J/(mol·K)) + (1.5 mol N2 × 20.8 J/(mol·K)) × (450 K - 298 K)
After calculating q, we can substitute the values into the formula for work done:
Work done = -5.72 * 10^3 kJ - q
Please note that the units of temperature used in the calculation must be in Kelvin (K) to maintain consistency in the equation.