THe following reaction is carried out in a bomb calorimeter:
4NH3(g )+ 5O2(g) ---> 4NO(g) + 6H20
The calorimeter constant is 45.0kJ/K. WHen 34.0g of NH3 are reacted in the calorimeter, the temperature rises by 10.0C. What is the change in energy, dE (where d is delta), for the reaction?
To find the change in energy (ΔE) for the reaction, we can use the equation:
ΔE = q - (C × ΔT)
Where:
q is the heat absorbed by the reaction,
C is the calorimeter constant,
ΔT is the change in temperature.
Given:
Mass of NH3 (m) = 34.0 g
Change in temperature (ΔT) = 10.0 °C
Calorimeter constant (C) = 45.0 kJ/K
Before we can calculate q, we need to find the heat absorbed by the reaction.
Step 1: Convert the mass of NH3 into moles.
To do this, we'll use the molecular weight of NH3.
Molecular weight of NH3 = (1 × 14.01 g/mol) + (3 × 1.008 g/mol) = 17.03 g/mol
Moles of NH3 (n) = mass / molecular weight
n = 34.0 g / 17.03 g/mol
n ≈ 1.995 mol (approximately 2.00 mol)
Now we know that 2.00 moles of NH3 reacted.
Step 2: Calculate the heat absorbed by the reaction (q).
To find q, we'll use the molar enthalpy change (ΔH) for the reaction.
From the balanced equation:
4NH3(g) + 5O2(g) → 4NO(g) + 6H2O
We can see that:
ΔH = (4 mol NO × ΔHf°NO) - (4 mol NH3 × ΔHf°NH3)
Given:
ΔHf°NO = unknown (we'll assume it to be x)
ΔHf°NH3 = -45.9 kJ/mol (standard enthalpy of formation of ammonia)
ΔH = (4 mol NO × x) - (4 mol NH3 × -45.9 kJ/mol)
ΔH = 4x + 183.6 kJ (equation 1)
Step 3: Calculate the heat absorbed by the reaction (q).
We'll use the formula q = ΔH × n.
q = ΔH × n
q = (4x + 183.6 kJ) × 2.00 mol
q = 8x + 367.2 kJ (equation 2)
Step 4: Calculate the change in energy (ΔE).
We'll use the formula ΔE = q - (C × ΔT).
ΔE = q - (C × ΔT)
ΔE = 8x + 367.2 kJ - (45.0 kJ/K × 10.0 °C)
ΔE = 8x + 367.2 kJ - 450.0 kJ
ΔE = 8x - 82.8 kJ (equation 3)
From equation 1, we know that ΔH = 4x + 183.6 kJ. We can substitute this value into equation 3 to solve for ΔE.
ΔE = 8x - 82.8 kJ
ΔE = 8(ΔH - 183.6 kJ) - 82.8 kJ
ΔE = 8ΔH - 1470.8 kJ
Finally, we can conclude that the change in energy (ΔE) for the reaction is 8ΔH - 1470.8 kJ.
To calculate the change in energy (ΔE) for the reaction, we can use the equation:
ΔE = q + CΔT
where q is the heat transferred, C is the calorimeter constant, and ΔT is the change in temperature.
Given data:
Mass of NH3 (m) = 34.0 g
Calorimeter constant (C) = 45.0 kJ/K
Change in temperature (ΔT) = 10.0 °C
Step 1: Convert the mass of NH3 to moles.
To do this, we need the molar mass of NH3.
Molar mass of NH3 = (1 * atomic mass of N) + (3 * atomic mass of H)
Molar mass of N = 14.01 g/mol
Molar mass of H = 1.01 g/mol
Molar mass of NH3 = (1 * 14.01 g/mol) + (3 * 1.01 g/mol)
Molar mass of NH3 = 17.03 g/mol
Now, we can calculate the number of moles of NH3:
moles of NH3 = mass of NH3 / molar mass of NH3
moles of NH3 = 34.0 g / 17.03 g/mol
moles of NH3 = 1.997 mol (rounded to three decimal places)
Step 2: Determine the heat transferred (q).
To find q, we can use the equation:
q = moles of NH3 * ΔH
where ΔH is the enthalpy change of the reaction. From the balanced equation:
4 NH3(g) + 5 O2(g) → 4 NO(g) + 6 H2O
we can see that the stoichiometry tells us that 4 moles of NH3 are required to produce 4 moles of NO. Therefore, the number of moles of NO produced is also 1.997 mol.
Step 3: Calculate the change in energy (ΔE).
Using the equation:
ΔE = q + CΔT
we can substitute the values we have:
ΔE = (moles of NH3 * ΔH) + CΔT
Given that ΔH is not provided in the question, we cannot calculate ΔE without this information. The enthalpy change (ΔH) can be obtained from a table or by performing an experiment.
So, to find the value of ΔE, we need to know the enthalpy change (ΔH) of the reaction.