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2 June, 10:01

A 0.500 g sample of TNT is burned in a bomb calorimeter containing 610 g of water at an initial temperature of 20.0 celcius. The heat capacity of the calorimeter is 420 J/C and the heat of combustion of TNT is 3374 kj/mol.

(a) Write and balance the chemical equation

(b) Using these data, calculate the final temperature of the water and calorimeter once the reaction is complete

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  1. 2 June, 10:10
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    a) 2C₇H₅N₃O₆ + 7O₂ → 3N₂ + 5H₂O + 7CO + 7CO₂

    b) 22.50°C

    Explanation:

    a) TNT has as molecular formula C₇H₅N₃O₆, and the explosion or combustion reaction produces nitrogen gas, water, carbon monoxide, and carbon dioxide as:

    C₇H₅N₃O₆ + O₂ → N₂ + H₂O + CO + CO₂

    To balance it, the number of elements must be the same on both sides of the equation. So, first, let's multiply each carbon product by 7, and C₇H₅N₃O₆ by 2:

    2C₇H₅N₃O₆ + O₂ → N₂ + H₂O + 7CO + 7CO₂

    Thus, N₂ must be multiplied by 3, and H₂O by 5:

    2C₇H₅N₃O₆ + O₂ → 3N₂ + 5H₂O + 7CO + 7CO₂

    And now O₂ by 7:

    2C₇H₅N₃O₆ + 7O₂ → 3N₂ + 5H₂O + 7CO + 7CO₂

    b) The calorimeter is an equipment used to calculate the energy released by combustion, and it can be considered isolated. By energy conservation:

    Qcombustion + Qcalorimeter + Qwater = 0

    The energy released of the combustion must be negative, the signal indicates that the heat is lost. The molar mass of TNT is 227.13 g/mol, thus the number of moles is:

    n = mass/molar mass

    n = 0.500/227.13 = 2.20x10⁻³ mol

    So,

    Qcombustion = - 3374 kJ/mol * 2.20x10⁻³ mol

    Qcombustion = - 7.4275 kJ = - 7427.5 J

    Qcalorimter = C*ΔT, where C is the heat capacity, and ΔT is the temperature variation (final - initial).

    Qwater = m*c*ΔT, where m is the mass, and c is the specific heat (4.184 J/g°C).

    Thus,

    -7427.5 + 420*ΔT + 610*4.184*ΔT = 0

    (420 + 2552.24) ΔT = 7427.5

    ΔT = 2.5

    Tfinal - 20.0 = 2.5

    Tfinal = 22.50°C
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